Book contents
- Frontmatter
- Preface
- Contents
- PART I PROOF THEORETIC ANALYSIS
- Ordinal analysis without proofs
- Relating ordinals to proofs in a perspicuous way
- Internal finite tree embeddings
- Foundational and mathematical uses of higher types
- The epsilon substitutionmethod and continuity
- Predicativity: The outer limits
- PART II LOGIC AND COMPUTATION
- PART III APPLICATIVE AND SELF-APPLICATIVE THEORIES
- PART IV PHILOSOPHY OF MODERN MATHEMATICAL AND LOGICAL THOUGHT
- Symposium program
- References
Foundational and mathematical uses of higher types
from PART I - PROOF THEORETIC ANALYSIS
Published online by Cambridge University Press: 31 March 2017
Book contents
- Frontmatter
- Preface
- Contents
- PART I PROOF THEORETIC ANALYSIS
- Ordinal analysis without proofs
- Relating ordinals to proofs in a perspicuous way
- Internal finite tree embeddings
- Foundational and mathematical uses of higher types
- The epsilon substitutionmethod and continuity
- Predicativity: The outer limits
- PART II LOGIC AND COMPUTATION
- PART III APPLICATIVE AND SELF-APPLICATIVE THEORIES
- PART IV PHILOSOPHY OF MODERN MATHEMATICAL AND LOGICAL THOUGHT
- Symposium program
- References
Summary
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- Reflections on the Foundations of MathematicsEssays in Honor of Solomon Feferman, pp. 92 - 116Publisher: Cambridge University PressPrint publication year: 2002
References
[1] , , Gödel's functional (‘Dialectica’) interpretation. In: [3], pp. 337-405.(1998).
[2] , Foundations of ConstructiveMathematics. Springer Ergebnisse derMathematik und ihrer Grenzgebiete 3.Folge, Bd.6., Berlin Heidelberg New York Tokyo (1985).
[3] (editor), Handbook of Proof Theory. Studies in Logic and the Foundations of Mathematics Vol 137, Elsevier, vii+811 pp. (1998).
[4] , Alanguage and axioms for explicit mathematics. In: (ed.), Algebra and Logic, pp. 87-139. Springer Lecture Notes in Mathematics 450 (1975).Google Scholar
[5] , Theories of finite type related to mathematical practice. In: |(ed.), Handbook of Mathematical Logic, pp. 913-972. North-Holland, Amsterdam (1977).
[6] , Working foundations. Synthese 62, pp. 229-254.(1985).
[7] , Weyl vindicated: Das Kontinuum seventy years later, in: , |(eds.), Temi e prospettive della logica e della filosofia della scienza contemporance, vol. I, pp. 59-93.(1988), CLUEB, Bologna. Reprinted (with minor additions) in [10].
[8] , Infinity in mathematics: Is Cantor necessary?. In: (ed.), L'infinito nella scienza, Istituto della Enciclopedia Italiana, Rome, pp. 151-209.(1987). Reprinted (with minor additions) in [10].
[9] , Why a little bit goes a long way: Logical foundations of scientifically applicable mathematics. In PSA (1992), Vol.2 (Philosophy of Science Association, East Lansing), pp. 442-455. Reprinted (with minor additions) in [10].
[10] , In the Light of Logic. Oxford University Press, 340 pp. (1998).
[11] , , Systems of explicit mathematics with non-constructive _-operator. Ann. Pure Applied Logic, Part I. 65, pp. 243-263.(1993), Part II. 79, pp. 37-52.(1996).Google Scholar
[12] , Models of ZF-Set Theory. Lecture Notes in Mathematics 223, Springer, Berlin (1971).
[13] , Über eine bisher noch nicht benutzte Erweiterung des finiten Standpunktes. Dialectica 12, pp. 280-287.(1958).Google Scholar
[14] , On effectively discontinuous type-2 objects. J. Symbolic Logic 36, pp. 245-248.(1971).
[14] , On effectively discontinuous type-2 objects. J. Symbolic Logic 36, pp. 245-248 (1971).
[15] Halpern|J.D., The Boolean Prime Ideal theorem does not imply the axiom of choice. In: Proc. of Symp. Pure Math. vol.XIII, pp.83-134, AMS, Providence (1971).
[16] , The axiom of choice and two definitions of continuity. Bull. Acad. Polon. Sci. 13, pp.699-704 (1965).Google Scholar
[17] , Remarks on Herbrand normal forms and Herbrand realizations. Arch. Math. Logic 31, pp. 305-317.(1992).Google Scholar
[18] , Pointwise hereditary majorization and some applications. Arch.Math. Logic 31, pp. 227-241.(1992).
[19] , Effective bounds from ineffective proofs in analysis: an application of functional interpretation and majorization. J. Symbolic Logic 57, pp. 1239-1273.(1992).Google Scholar
[20] , Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation. Ann. Pure Appl. Logic 64, pp. 27-94.(1993).
[21] , Analysing proofs in analysis. In: , , , , editors, Logic: from Foundations to Applications. European Logic Colloquium (Keele, 1993), pp. 225-260. Oxford University Press (1996).
[22] , Real growth in standard parts of analysis. Habilitationsschrift, pp. xv+166, Frankfurt (1995).
[23] , Mathematically strong subsystems of analysis with low rate of growth of provably recursive functionals. Arch. Math. Logic 36, pp. 31-71.(1996).Google Scholar
[24] , Proof theory and computational analysis. Electronic Notes in Theoretical Computer Science 13, Elsevier (http://www.elsevier.nl/locate/entcs/volume13.html), (1998).
[25] , The use of a logical principle of uniformboundedness in analysis. In: , , (eds.), Logic and Foundations of Mathematics. Synthese Library 280, pp. 93-106. Kluwer Academic Publishers (1999).
[26] , Arithmetizing proofs in analysis. In: et al. (eds.), Proceedings Logic Colloquium 96 (San Sebastian), Springer Lecture Notes in Logic 12, pp. 115-158.(1998).
[27] , On the arithmetical content of restricted forms of comprehension, choice and general uniform boundedness. Ann. Pure and Applied Logic 95, pp. 257-285.(1998).Google Scholar
[28] , On the no-counterexample interpretation. J. Symbolic Logic 64, pp. 1491- 1511.(1999).Google Scholar
[29] , Things that can and things that can't be done in PRA. Ann. Pure Applied Logic 102, pp. 223-245.(2000).Google Scholar
[30] , On the uniform weak König's lemma. To appear in: Annals of Pure Applied Logic.
[31] , Higher order reverse mathematics. Preprint 14pp., submitted.
[32] , Recursion on the Countable Functionals. Springer Lecture Notes in Mathematics 811 (1980).Google Scholar
[34] , Partial realizations of Hilbert's program. J. Symbolic Logic 53, 349-363 (1988).Google Scholar
[35] , Subsystems of Second Order Arithmetic. Perspectives inMathematical Logic. Springer-Verlag. xiv+445 pp. (1999).
[37] , A conservative extension of Peano arithmetic. Part II of ‘Two applications of logic to mathematics’, Publ. Math. Soc. Japan 13, (1978).Google Scholar
[38] (ed.)Metamathematical investigation of intuitionistic arithmetic and analysis. Springer Lecture Notes inMathematics 344 (1973).Google Scholar
[40] , . Kritische Untersuchungenüber die Grundlagen der Analysis. Veit, Leipzig (1918). English translation: , The Continuum: A critical Examination of the Foundation of Analysis. New York, Dover (1994).
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