Items where authors include "Rathjen, M"

Article

Rathjen, M orcid.org/0000-0003-1699-4778 (2023) Ordinal analysis and the set existence property for intuitionistic set theories. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 381 (2248). 20220019. ISSN 1364-503X

Maietti, ME, Maschio, S and Rathjen, M orcid.org/0000-0003-1699-4778 (2022) Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice. Logical Methods in Computer Science, 18 (4). 5:1-5:28. ISSN 1860-5974

Aguilera, JP, Freund, A, Rathjen, M orcid.org/0000-0003-1699-4778 et al. (1 more author) (2022) Boundedness theorems for flowers and sharps. Proceedings of the American Mathematical Society, 150 (9). pp. 3973-3988. ISSN 0002-9939

Freund, A, Rathjen, M orcid.org/0000-0003-1699-4778 and Weiermann, A (2022) Minimal bad sequences are necessary for a uniform Kruskal theorem. Advances in Mathematics, 400. 108265. ISSN 0001-8708

Aguilera, JP, Freund, A, Rathjen, M orcid.org/0000-0003-1699-4778 et al. (1 more author) (2021) Ackermann and Goodstein go functorial. Pacific Journal of Mathematics, 313 (2). pp. 251-291. ISSN 0030-8730

Maietti, ME, Maschio, S and Rathjen, M (2021) A realizability semantics for inductive formal topologies, church’s thesis and axiom of choice. Logical Methods in Computer Science, 17 (2). 21:1-21:21. ISSN 1860-5974

Freund, A and Rathjen, M (2021) Derivatives of normal functions in reverse mathematics. Annals of Pure and Applied Logic, 172 (2). 102890. ISSN 0168-0072

Frittaion, E and Rathjen, M (2020) Extensional realizability for intuitionistic set theory. Journal of Logic and Computation. exaa087. ISSN 0955-792X

Rathjen, M and Swan, AW (2020) Lifschitz Realizability as a Topological Construction. The Journal of Symbolic Logic, 85 (4). pp. 1342-1375. ISSN 0022-4812

Rathjen, M orcid.org/0000-0003-1699-4778 (2020) Power Kripke–Platek set theory and the axiom of choice. Journal of Logic and Computation, 30 (1). pp. 447-457. ISSN 0955-792X

Dihoum, E and Rathjen, M (2019) Preservation of choice principles under realizability. Logic Journal of the IGPL, 27 (5). pp. 746-765. ISSN 1367-0751

Rathjen, M (2019) The scope of Feferman’s semi-intuitionistic set theories and his second conjecture. Indagationes Mathematicae, 30 (3). pp. 500-525. ISSN 0019-3577

Rathjen, M (2017) Long Sequences of Descending Theories and Other Misellanea on Slow Consistency. IfCoLoG Journal of Logics and their Applications, 4 (4). pp. 1411-1426. ISSN 2055-3706

Rathjen, M, Van Der Meeren, J and Weiermann, A (2017) Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition. Archive for Mathematical Logic, 56 (5-6). pp. 607-638. ISSN 0933-5846

Van der Meeren, J, Rathjen, M and Weiermann, A (2017) An order-theoretic characterization of the Howard-Bachmann-hierarchy. Archive for Mathematical Logic, 56 (1). pp. 79-118. ISSN 0933-5846

Cook, J and Rathjen, M (2016) Classifying the provably total set functions of KP and KP(P). IfCoLog Journal of Logics and their Applications, 3 (4). pp. 681-753. ISSN 2055-3706

Rathjen, M (2016) Indefiniteness in semi-intuitionistic set theories: On a conjecture of Feferman. Journal of Symbolic Logic, 81 (2). pp. 742-754. ISSN 0022-4812

Van der Meeren, J, Rathjen, M and Weiermann, A (2014) Well-partial-orderings and the big Veblen number. Archive for Mathematical Logic. ISSN 0933-5846

Rathjen, M (2014) Relativized ordinal analysis: The case of Power Kripke-Platek set theory. Annals of Pure and Applied Logic, 165 (1). 316 - 339. ISSN 0168-0072

Rathjen, M (2013) Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience. Annals of Pure and Applied Logic, 165 (2). 563 - 572. ISSN 0168-0072

Friedman, S-D, Rathjen, M and Weiermann, A (2013) Slow consistency. Annals of Pure and Applied Logic, 164 (3). 382 - 393 (12). ISSN 0168-0072

Rathjen, M (2012) From the weak to the strong existence property. Annals of Pure and Applied Logic, 163 (10). 1400 - 1418 (19). ISSN 0168-0072

Chen, R-M and Rathjen, M (2012) Lifschitz realizability for intuitionistic Zermelo-Fraenkel set theory. Archive for Mathematical Logic, 51 (7-8). 789 - 818 (20). ISSN 0933-5846

Rathjen, M and Leigh, GE (2012) The Friedman-Sheard programme in intuitionistic logic. The Journal of Symbolic Logic, 77 (3). 777 - 806 (30). ISSN 0022-4812

Rathjen, M and Lubarsky, RS (2008) On the constructive Dedekind reals. Logic and Analysis, 1 (1). 131 - 152 (23). ISSN 1759-9008

Rathjen, M (2005) Constructive set theory and Brouwerian principles. Journal of Universal Computer Science, 11 (12). 2008 - 2033. ISSN 0948-695X

Book Section

Rathjen, M (2022) Well-Ordering Principles in Proof Theory and Reverse Mathematics. In: Ferreira, F, Kahle, R and Sommaruga, G, (eds.) Axiomatic Thinking II. Springer , pp. 89-127. ISBN 978-3-030-77798-2

Rathjen, M orcid.org/0000-0003-1699-4778 and Tupailo, S (2020) On the Strength of the Uniform Fixed Point Principle in Intuitionistic Explicit Mathematics. In: Kahle, R and Rathjen, M, (eds.) The Legacy of Kurt Schütte. Springer , pp. 377-399. ISBN 978-3-030-49423-0

Rathjen, M and Thomson, IA (2020) Well-ordering principles, omega-models and Pi-1-1-comprehension. In: Kahle, R and Rathjen, M, (eds.) The Legacy of Kurt Schütte. Springer , pp. 171-215. ISBN 978-3-030-49423-0

Krombholz, M and Rathjen, M (2020) Upper Bounds on the Graph Minor Theorem. In: Schuster, P, Seisenberger, M and Weiermann, A, (eds.) Well-Quasi Orders in Computation, Logic, Language and Reasoning: A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory. Springer International Publishing , pp. 145-159. ISBN 978-3030302283

Rathjen, M (2017) Proof Theory of Constructive Systems: Inductive Types and Univalence. In: Jaeger, G and Sieg, W, (eds.) Feferman on Foundations: Logic, Mathematics, Philosophy. Outstanding Contributions to Logic . Springer , pp. 385-419. ISBN 978-3-319-63332-9

Rathjen, M (2016) Remarks on Barr's theorem : Proofs in geometric theories. In: Probst, D and Schuster, P, (eds.) Concepts of Proof in Mathematics, Philosophy, and Computer Science. Walter de Gruyter , pp. 347-373. ISBN 978-1-5015-0262-0

Cook, J and Rathjen, M (2016) Ordinal Analysis of Intuitionistic Power and Exponentiation Kripke Platek Set Theory. In: Kahle, R, Strahm, T and Studer, T, (eds.) Advances in Proof Theory. Progress in Computer Science and Applied Logic, 28 . Springer International Publishing , Cham, Switzerland , pp. 79-172. ISBN 978-3-319-29196-3

Rathjen, M (2015) Goodstein's theorem revisited. In: Kahle, R and Rathjen, M, (eds.) Gentzen's Centenary: The Quest for Consistency. Springer International Publishing , London , pp. 229-242. ISBN 3319101021

Rathjen, M and Vizcaino, PFV (2015) Well-Ordering Principles and Bar Induction. In: Kahle, R and Rathjen, M, (eds.) Gentzen's Centenary: The Quest for Consistency. Springer International Publishing , London , pp. 533-561. ISBN 978-3-319-10102-6

Rathjen, M (2014) Omega-models and well-ordering proofs. In: Tennant, N, (ed.) Foundational Adventures. College Publications , 179 - 212. ISBN 978-1-84890-117-9

Rathjen, M (2012) Constructive zermelo-fraenkel set theory, power set, and the calculus of constructions. In: Dybjer, P, Lindström, S, Palmgren, E and Sundholm, G, (eds.) Epistemology versus ontology: Essays on the philosophy and foundations of mathematics in honour of Per Martin-Löf. Logic, Epistemology, and the Unity of Science, 27 . Springer , Dordrecht, Netherlands , 313 - 349. ISBN 9789400744356

Curi, G and Rathjen, M (2012) Baire space in CZF. In: Berger, U, Diener, H, Schuster, P and Seisenberger, M, (eds.) Logic, construction, computation. Ontos Verlag , 123 - 135. ISBN 978-3-11-032492-1

Rathjen, M (2010) Investigations of subsystems of second order arithmetic and set theory in strength between Pi-1-1-CA and delta-1-2-CA+BI: part I. In: Ways of proof theory. Walter de Gruyter , 363 - 440. ISBN 978-3-86838-087-3

Rathjen, M (2010) Metamathematical properties of intuitionistic set theories with choice principles. In: Cooper, SB, Lowe, B and Sorbi, A, (eds.) New Computational Paradigms: Changing Conceptions of What is Computable. Springer , 287 - 312. ISBN 978-1-4419-2263-2

Proceedings Paper

Krombholz, M and Rathjen, M (2020) Upper Bounds on the Graph Minor Theorem. In: Schuster, P, Seisenberger, M and Weiermann, A, (eds.) Well-Quasi Orders in Computation, Logic, Language and Reasoning: A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory. Well Quasi-Orders in Computer Science (Dagstuhl Seminar 16031), 17-22 Jan 2016, Dagstuhl, Germany. Trends in Logic, 53 . Springer , pp. 145-160. ISBN 978-3-030-30228-3

Rathjen, M orcid.org/0000-0003-1699-4778 and Toppel, M (2019) On Relating Theories: Proof-Theoretical Reduction. In: Centrone, S, Negri, S, Sarikaya, D and Schuster, PM, (eds.) Mathesis Universalis, Computability and Proof. Humboldt-Kolleg: Proof Theory as Mathesis Universalis, 24-28 Jul 2017, Loveno di Menaggio (Como), Italy. Springer , pp. 311-331. ISBN 978-3-030-20446-4

Carlucci, L, Mainardi, L and Rathjen, M (2019) A Note on the Ordinal Analysis of RCA0+WO(σ). In: Manea, F, Martin, B, Paulusma, D and Primiero, G, (eds.) Lecture Notes in Computer Science. Computability in Europe 2019: Computing with Foresight and Industry, 15-19 Jul 2019, Durham, UK. Springer , Cham, Switzerland , pp. 144-155. ISBN 978-3-030-22995-5