@inbook{jae18,
title = {The Operational Penumbra: Some Ontological Aspects},
booktitle = {Feferman on Foundations - Logic, Mathematics, Philosophy},
volume = {13},
year = {2018},
publisher = {Springer International Publishing},
organization = {Springer International Publishing},
pdf = {https://home.inf.unibe.ch/ltg/publications/2018/jae18.pdf},
author = {J{\"a}ger, Gerhard}
}
@conference{jmidk16,
title = {A canonical model construction for intuitionistic distributed knowledge},
booktitle = {Advances in Modal Logic 2016},
year = {2016},
publisher = {College Publications},
organization = {College Publications},
pdf = {https://home.inf.unibe.ch/ltg/publications/2016/jmidk16.pdf},
author = {J{\"a}ger, Gerhard and Marti, Michel}
}
@article{jae15,
title = {Relativizing operational set theory},
journal = {The Bulletin of Symbolic Logic},
year = {2016},
abstract = {We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST(LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST(LR) is proof- eoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.},
pdf = {https://home.inf.unibe.ch/ltg/publications/2015/jae15.pdf},
author = {J{\"a}ger, Gerhard}
}
@incollection{bjs15,
volume = {6},
month = jan,
author = {Buchholtz, Ulrik Torben and J{\"a}ger, Gerhard and Strahm, Thomas Adrian},
series = {Ontos Mathematical Logic},
booktitle = {Concepts of Proof in Mathematics, Philosophy, and ComputerScience},
editor = {Probst, Dieter and Schuster, Peter},
title = {Theories of proof-theoretic strength {$\psi$}({$\Gamma$}?+1)},
publisher = {De Gruyter},
year = {2016},
journal = {Ontos Mathematical Logic},
isbn = {978-1-5015-0263-7},
pdf = {https://home.inf.unibe.ch/ltg/publications/2015/bjs15.pdf},
month_numeric = {1}
}
@article{jmick15,
title = {Intuitionistic common knowledge or belief},
author = {J{\"a}ger, Gerhard and Marti, Michel},
publisher = {Elsevier},
year = {2016},
journal = {Journal of applied logic},
pdf = {https://home.inf.unibe.ch/ltg/publications/2015/jmick15.pdf},
abstract = {Starting off from the usual language of modal logic for multi-agent systems dealing with the agents? knowledge/belief and common knowledge/belief we define so-called epistemic Kripke structures for intu- itionistic (common) knowledge/belief. Then we introduce corresponding deductive systems and show that they are sound and complete with respect to these semantics.}
}
@inproceedings{hjss95a,
author = {Heuerding, Alain and J{\"a}ger, Gerhard and Schwendimann, Stefan and Seyfried, Michael},
title = {Propositional logics on the computer},
booktitle = {Proceedings of Theorem Proving with Analytic Tableaux and Related Methods},
editor = {Baumgartner, Peter and H{\"a}hnle, Reiner and Posegga, Joachim},
volume = {918},
series = {Lecture Notes in Computer Science},
pages = {310{--}323},
publisher = {Springer},
ps = {https://home.inf.unibe.ch/ltg/publications/1995/hjss95a.ps},
year = {1995}
}
@article{jks01,
author = {J{\"a}ger, Gerhard and Kahle, Reinhard and Studer, Thomas},
title = {Universes in explicit mathematics},
journal = {Annals of Pure and Applied Logic},
volume = {109},
number = {3},
pages = {141{--}162},
pdf = {https://home.inf.unibe.ch/ltg/publications/2001/jks01.pdf},
year = {2001}
}
@article{jz14,
author = {J{\"a}ger, Gerhard and Zumbrunnen, Rico},
title = {{Explicit mathematics and operational set theory: some ontological comparisons}},
journal = {The Bulletin of Symbolic Logic},
volume = {20},
issue = {03},
month = sep,
year = {2014},
issn = {1943-5894},
pages = {275--292},
numpages = {18},
doi = {10.1017/bsl.2014.21},
pdf = {https://home.inf.unibe.ch/ltg/publications/2014/jz14.pdf},
month_numeric = {9}
}
@article{jae13,
author = {J{\"a}ger, Gerhard},
title = {Operational closure and stability},
journal = {Annals of Pure and Applied Logic},
volume = {164},
number = {7–8},
pages = {813 - 821},
year = {2013},
issn = {0168-0072},
doi = {http://dx.doi.org/10.1016/j.apal.2013.01.004},
pdf = {https://home.inf.unibe.ch/ltg/publications/2013/jae13.pdf},
abstract = {In this article we introduce and study the notion of operational closure: a transitive set d is called operationally closed iff it contains all constants of $\mathsf{OST}$ and any operation $f\in d$ applied to an element $a\in d$ yields an element $fa\in d$ , provided that $f$ applied to a has a value at all. We will show that there is a direct relationship between operational closure and stability in the sense that operationally closed sets behave like $\Sigma_1$ substructures of the universe. This leads to our final result that $\mathsf{OST}$ plus the axiom $(\mathsf{OLim})$ , claiming that any set is element of an operationally closed set, is proof-theoretically equivalent to the system $\mathsf{KP}+(\Sigma_1\text{-}\mathsf{Sep})$ of Kripke-Platek set theory with infinity and $\Sigma_1$ separation. We also characterize the system $\mathsf{OST}$ plus the existence of one operationally closed set in terms of Kripke-Platek set theory with infinity and a parameter-free version of $\Sigma_1$ separation.}
}
@inproceedings{jz12,
author = {J{\"a}ger, Gerhard and Zumbrunnen, Rico},
title = {{About the Strength of Operational Regularity}},
pages = {305{--}324},
editor = {Berger, Ulrich and Diener, Hannes and Schuster, Peter and Seisenberger, Monika},
booktitle = {Logic, Construction, Computation},
year = {2012},
publisher = {Ontos Verlag},
pdf = {https://home.inf.unibe.ch/ltg/publications/2012/jz12.pdf}
}
@article{js00,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {Fixed point theories and dependent choice},
journal = {Archive for Mathematical Logic},
volume = {39},
number = {7},
pages = {493{--}508},
ps = {https://home.inf.unibe.ch/ltg/publications/2000/js00.ps},
year = {2000}
}
@article{js95a,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {Second order theories with ordinals and elementary comprehension},
journal = {Archive for Mathematical Logic},
volume = {34},
number = {6},
pages = {345{--}375},
ps = {https://home.inf.unibe.ch/ltg/publications/1995/js95a.ps},
year = {1995}
}
@article{aj05,
author = {Alberucci, Luca and J{\"a}ger, Gerhard},
title = {About cut elimination for logics of common knowledge},
journal = {Annals of Pure and Applied Logic},
volume = {133},
number = {1{--}3},
pages = {73{--}99},
doi = {10.1016/j.apal.2004.10.004},
pdf = {https://home.inf.unibe.ch/ltg/publications/2005/aj05.pdf},
year = {2005}
}
@article{js02b,
author = {J{\"a}ger, Gerhard and Studer, Thomas},
title = {Extending the system $\mathsf{T}_{0}$ of explicit mathematics: the limit and {M}ahlo axioms},
journal = {Annals of Pure and Applied Logic},
volume = {114},
number = {1{--}3},
pages = {79{--}101},
pdf = {https://home.inf.unibe.ch/ltg/publications/2002/js02b.pdf},
year = {2002}
}
@article{jae07,
author = {J{\"a}ger, Gerhard},
title = {On {F}eferman's operational set theory $\mathsf{OST}$},
journal = {Annals of Pure and Applied Logic},
volume = {150},
number = {1{--}3},
pages = {19{--}39},
pdf = {https://home.inf.unibe.ch/ltg/publications/2007/jae07.pdf},
year = {2007}
}
@article{js05,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {Reflections on reflections in explicit mathematics},
journal = {Annals of Pure and Applied Logic},
volume = {136},
number = {1{--}2},
pages = {116{--}133},
pdf = {https://home.inf.unibe.ch/ltg/publications/2005/js05.pdf},
year = {2005}
}
@incollection{jae97b,
author = {J{\"a}ger, Gerhard},
title = {Some proof theory of first order logic programming},
booktitle = {Logic of Computation},
publisher = {Springer},
editor = {Schwichtenberg, Helmut},
volume = {157},
series = {{NATO} Science Series},
pages = {201{--}228},
year = {1997}
}
@article{hj94,
author = {H{\"o}sli, Brigitte and J{\"a}ger, Gerhard},
title = {About some symmetries of negation},
journal = {The Journal of Symbolic Logic},
volume = {59},
number = {2},
pages = {473{--}485},
url = {http://www.jstor.org/stable/2275401},
year = {1994}
}
@article{js96,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {Some theories with positive induction of ordinal strength $\varphi \omega 0$},
journal = {The Journal of Symbolic Logic},
volume = {61},
number = {3},
pages = {818{--}842},
ps = {https://home.inf.unibe.ch/ltg/publications/1996/js96.ps},
year = {1996}
}
@article{jae01,
author = {J{\"a}ger, Gerhard},
title = {First order theories for nonmonotone inductive definitions: recursively inaccessible and {M}ahlo},
journal = {The Journal of Symbolic Logic},
volume = {66},
number = {3},
pages = {1073{--}1089},
pdf = {https://home.inf.unibe.ch/ltg/publications/2001/jae01.pdf},
year = {2001}
}
@inproceedings{jae95,
author = {J{\"a}ger, Gerhard},
title = {A deductive approach to logic programming},
booktitle = {Proof and Computation},
editor = {Schwichtenberg, Helmut},
volume = {139},
series = {NATO ASI Series F},
pages = {231{--}270},
publisher = {Springer},
year = {1995}
}
@article{js95b,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {Totality in applicative theories},
journal = {Annals of Pure and Applied Logic},
volume = {74},
number = {2},
pages = {105{--}120},
ps = {https://home.inf.unibe.ch/ltg/publications/1995/js95b.ps},
year = {1995}
}
@inproceedings{jae93b,
author = {J{\"a}ger, Gerhard},
title = {Some proof-theoretic aspects of logic programming},
booktitle = {Logic and Algebra of Specification},
editor = {Bauer, Friedrich Ludwig and Brauer, Wilfried and Schwichtenberg, Helmut},
volume = {94},
series = {Computer and Systems Sciences},
pages = {113{--}142},
publisher = {Springer},
year = {1993}
}
@article{fj96,
author = {Feferman, Solomon and J{\"a}ger, Gerhard},
title = {Systems of explicit mathematics with non-constructive $\mu$-operator. {P}art {II}},
journal = {Annals of Pure and Applied Logic},
volume = {79},
number = {1},
pages = {37{--}52},
doi = {10.1016/0168-0072(95)00028-3},
url = {http://dx.doi.org/10.1016/0168-0072(95)00028-3},
year = {1996}
}
@article{jae97a,
author = {J{\"a}ger, Gerhard},
title = {Power types in explicit mathematics?},
journal = {The Journal of Symbolic Logic},
volume = {62},
number = {4},
pages = {1142{--}1146},
url = {http://www.jstor.org/stable/2275630},
year = {1997}
}
@incollection{jks99,
author = {J{\"a}ger, Gerhard and Kahle, Reinhard and Strahm, Thomas},
title = {On applicative theories},
booktitle = {Logic and Foundations of Mathematics},
publisher = {Kluwer},
editor = {Cantini, Andrea and Casari, Ettore and Minari, Pierluigi},
pages = {83{--}92},
ps = {https://home.inf.unibe.ch/ltg/publications/1999/jks99.ps},
year = {1999}
}
@article{hjss96a,
author = {Heuerding, Alain and J{\"a}ger, Gerhard and Schwendimann, Stefan and Seyfried, Michael},
title = {A logics workbench},
journal = {The European Journal on Artificial Intelligence},
volume = {9},
number = {2},
pages = {53{--}58},
year = {1996}
}
@inproceedings{jp04a,
author = {J{\"a}ger, Gerhard and Probst, Dieter},
title = {Iterating ${\Sigma}$ operations in admissible set theory without foundation: a further aspect of metapredicative {M}ahlo},
booktitle = {One Hundred Years of Russell's Paradox. Papers from the 2001 Munich Russell Conference},
editor = {Link, Godehart},
pages = {119{--}134},
publisher = {de Gruyter},
pdf = {https://home.inf.unibe.ch/ltg/publications/2004/jp04a.pdf},
year = {2004}
}
@incollection{js98,
author = {J{\"a}ger, Gerhard and St{\"a}rk, Robert F.},
title = {A proof-theoretic framework for logic programming},
booktitle = {Handbook of Proof Theory},
publisher = {North-Holland},
editor = {Buss, Samuel S.},
pages = {639{--}682},
doi = {10.1016/S0049-237X(98)80024-4},
url = {http://dx.doi.org/10.1016/S0049-237X(98)80024-4},
year = {1998}
}
@inproceedings{jks05,
author = {J{\"a}ger, Gerhard and Kretz, Mathis and Studer, Thomas},
title = {Cut-free axiomatizations for stratified modal fixed point logic},
booktitle = {Proceedings of Methods for Modalities 4},
editor = {Schlingloff, Holger},
volume = {194},
series = {Humboldt-Universit{\"a}t Berlin Informatik-Berichte},
pages = {125{--}143},
publisher = {Humboldt-Universit{\"a}t Berlin},
pdf = {https://home.inf.unibe.ch/ltg/publications/2005/jks05.pdf},
year = {2005}
}
@article{jks08,
author = {J{\"a}ger, Gerhard and Kretz, Mathis and Studer, Thomas},
title = {Canonical completeness of infinitary mu},
journal = {Journal of Logic and Algebraic Programming},
volume = {76},
number = {2},
pages = {270-292},
abstract = {},
doi = {10.1016/j.jlap.2008.02.005},
pdf = {https://home.inf.unibe.ch/ltg/publications/2008/jks08.pdf},
year = {2008}
}
@article{JS11,
author = {J{\"a}ger, Gerhard and Studer, Thomas},
title = {A {B}uchholz rule for modal fixed point logics},
journal = {Logica Universalis},
volume = {5},
number = {1},
pages = {1--19},
doi = {10.1007/s11787-010-0022-1},
pdf = {https://home.inf.unibe.ch/ltg/publications/2011/js11.pdf},
year = {2011}
}
@inproceedings{jae10,
author = {J{\"a}ger, Gerhard},
title = {Modal {F}ixed {P}oint {L}ogics},
booktitle = {Logics and {L}anguages for {R}eliability and {S}ecurity},
editor = {{J. Esparza} and {B. Spanfelner} and {O. Grumberg}},
volume = {25},
series = {NATO Science for Peace and Security Series - D: Information and Communication Security},
publisher = {IOS Press},
doi = {10.3233/978-1-60750-100-8-129},
pdf = {https://home.inf.unibe.ch/ltg/publications/2010/jae10.pdf},
year = {2010}
}
@inproceedings{hjss95b,
author = {Heuerding, Alain and J{\"a}ger, Gerhard and Schwendimann, Stefan and Seyfried, Michael},
title = {{LWB} - a logics workbench, extended abstract},
booktitle = {Proceedings of KI-95 Activities: Workshop, Posters, Demos},
editor = {Dreschler-Fischer, L. and Pribbenow, S.},
pages = {73{--}74},
publisher = {Gesellschaft f{\"u}r Informatik},
year = {1995}
}
@article{js01,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {Upper bounds for metapredicative {M}ahlo in explicit mathematics and admissible set theory},
journal = {The Journal of Symbolic Logic},
volume = {66},
number = {2},
pages = {935{--}958},
pdf = {https://home.inf.unibe.ch/ltg/publications/2001/js01.pdf},
year = {2001}
}
@article{hjss96b,
author = {Heuerding, Alain and J{\"a}ger, Gerhard and Schwendimann, Stefan and Seyfried, Michael},
title = {The logics workbench {LWB}: a snapshot},
journal = {Euromath Bulletin},
volume = {2},
number = {1},
pages = {177{--}186},
ps = {https://home.inf.unibe.ch/ltg/publications/1996/hjss96b.ps},
year = {1996}
}
@article{jp11,
author = {J{\"a}ger, Gerhard and Probst, Dieter},
title = {The Suslin operator in applicative theories: Its proof-theoretic analysis via ordinal theories},
journal = {Annals of Pure and Applied Logic},
volume = {162},
number = {8},
pages = {647--660},
doi = {10.1016/j.apal.2011.01.009},
issn = {0168-0072},
keywords = {Proof theory, Suslin operator in applicative theories, Ordinal theories},
pdf = {https://home.inf.unibe.ch/ltg/publications/2011/jp11.pdf},
year = {2011}
}
@article{jae04,
author = {J{\"a}ger, Gerhard},
title = {An intensional fixed point theory over first order arithmetic},
journal = {Annals of Pure and Applied Logic},
volume = {128},
number = {1{--}3},
pages = {197{--}213},
pdf = {https://home.inf.unibe.ch/ltg/publications/2004/jae04.pdf},
year = {2004}
}
@article{jae09a,
author = {J{\"a}ger, Gerhard},
title = {Full operational set theory with unbounded existential quantification and power set},
journal = {Annals of Pure and Applied Logic},
volume = {160},
number = {1},
pages = {33--52},
month = jul,
pdf = {https://home.inf.unibe.ch/ltg/publications/2009/jae09a.pdf},
year = {2009},
month_numeric = {7}
}
@incollection{jk10,
author = {J{\"a}ger, Gerhard and Kr{\"a}henb{\"u}hl, J{\"u}rg},
title = {${\Sigma^1_1}$ choice in a theory of sets and classes},
booktitle = {Ways of {P}roof {T}heory},
publisher = {Ontos Verlag},
editor = {{Ralf Schindler}},
pages = {283--314},
pdf = {https://home.inf.unibe.ch/ltg/publications/2010/jk10.pdf},
year = {2010}
}
@article{jp04b,
author = {J{\"a}ger, Gerhard and Probst, Dieter},
title = {Variation on a theme of {S}ch{\"u}tte},
journal = {Mathematical Logic Quarterly},
volume = {50},
number = {3},
pages = {258{--}264},
pdf = {https://home.inf.unibe.ch/ltg/publications/2004/jp04b.pdf},
year = {2004}
}
@article{fj93,
author = {Feferman, Solomon and J{\"a}ger, Gerhard},
title = {Systems of explicit mathematics with non-constructive $\mu$-operator. {P}art {I}},
journal = {Annals of Pure and Applied Logic},
volume = {65},
number = {3},
pages = {243{--}263},
pdf = {https://home.inf.unibe.ch/ltg/publications/1993/fj93.pdf},
year = {1993}
}
@article{js93,
author = {J{\"a}ger, Gerhard and St{\"a}rk, Robert F.},
title = {The defining power of stratified and hierarchical logic programs},
journal = {Journal of Logic Programming},
volume = {15},
number = {1{--}2},
pages = {55{--}77},
pdf = {https://home.inf.unibe.ch/ltg/publications/1993/js93.pdf},
year = {1993}
}
@article{jkss99,
author = {J{\"a}ger, Gerhard and Kahle, Reinhard and Setzer, Anton and Strahm, Thomas},
title = {The proof-theoretic analysis of transfinitely iterated fixed point theories},
journal = {The Journal of Symbolic Logic},
volume = {64},
number = {1},
pages = {53{--}67},
pdf = {https://home.inf.unibe.ch/ltg/publications/1999/jkss99.ps},
year = {1999}
}
@inproceedings{bejklm94,
author = {B{\"u}tler, B. and Esser, R. and J{\"a}ger, Gerhard and K{\"u}nzi, Urs-Martin and Lienhard, Heinz and Mattmann, R.},
title = {Executable models for analysis and implementation of complex systems},
booktitle = {Proceedings of Information Conference of Swiss Priority Programme Informatics Research 1992{--}1996, Module 1: Secure Distributed Systems},
year = {1994}
}
@article{js99,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {Bar induction and $\omega$ model reflection},
journal = {Annals of Pure and Applied Logic},
volume = {97},
number = {1{--}3},
pages = {221{--}230},
pdf = {https://home.inf.unibe.ch/ltg/publications/1999/js99.ps},
year = {1999}
}
@inproceedings{jae05,
author = {J{\"a}ger, Gerhard},
title = {Metapredicative and explicit {M}ahlo: a proof-theoretic perspective},
booktitle = {Proceedings of Logic Colloquium '00},
editor = {Cori, Rene and Razborov, Alexander and Todorcevic, Stevo and Wood, Carol},
volume = {19},
series = {Association of Symbolic Logic Lecture Notes in Logic},
pages = {272{--}293},
publisher = {AK Peters},
pdf = {https://home.inf.unibe.ch/ltg/publications/2005/jae05.pdf},
year = {2005}
}
@article{jae93a,
author = {J{\"a}ger, Gerhard},
title = {Fixed points in {P}eano arithmetic with ordinals},
journal = {Annals of Pure and Applied Logic},
volume = {60},
number = {2},
pages = {119{--}132},
doi = {10.1016/0168-0072(93)90039-G},
url = {http://dx.doi.org/10.1016/0168-0072(93)90039-G},
year = {1993}
}
@inproceedings{jae09b,
author = {J{\"a}ger, Gerhard},
title = {Operations, sets and classes},
booktitle = {Logic, {M}ethodology and {P}hilosophy of {S}cience - {P}roceedings of the {T}hirteenth {I}nternational {C}ongress},
editor = {{C. Glymour} and {W. Wei} and {D. Westerstahl}},
publisher = {College Publications},
pdf = {https://home.inf.unibe.ch/ltg/publications/2009/jae09b.pdf},
year = {2009}
}
@incollection{js02a,
author = {J{\"a}ger, Gerhard and Strahm, Thomas},
title = {The proof-theoretic analysis of the {S}uslin operator in applicative theories},
booktitle = {Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman},
publisher = {AK Peters},
editor = {Sieg, Wilfried and Sommer, Richard and Talcott, Carolyn},
pages = {270{--}292},
pdf = {https://home.inf.unibe.ch/ltg/publications/2002/js02a.pdf},
year = {2002}
}
@article{jks07,
author = {J{\"a}ger, Gerhard and Kretz, Mathis and Studer, Thomas},
title = {Cut-free common knowledge},
journal = {Journal of Applied Logic},
volume = {5},
number = {4},
pages = {681{--}689},
doi = {10.1016/j.jal.2006.02.003},
pdf = {https://home.inf.unibe.ch/ltg/publications/2007/jks07.pdf},
year = {2007}
}
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