endobj endobj (Idea of the proof) 160 0 obj << /S /GoTo /D (subsection.5.1.3) >> (Interpretation of Types) << /S /GoTo /D (section.9.2) >> (Linear implication) endobj endobj 40 0 obj << /S /GoTo /D (subsection.10.3.1) >> << /S /GoTo /D (subsection.7.1.1) >> endobj 362 0 obj endobj 222 0 obj 60 0 obj 538 0 obj 370 0 obj 694 0 obj %�6^�J���-�g�Bm,A������+[)���a��f�f�@��Z#�Q��# g{�� ���ION�����G�!�J;�e��d>�%���%��u՟R�Sцd�*��xS��ϯx�Y/+]�X�i��rL�=���X�K�D�}���Uh����������s�VzE��r�B����-.��dY�yK��4�q���� (Linear numerals) endobj endobj 554 0 obj /Length 234 endobj 144 0 obj endobj 464 0 obj 218 0 obj << /S /GoTo /D (section.11.4) >> endobj << /S /GoTo /D (subsection.A.3.1) >> endobj endobj endobj In a talk to theSwiss Mathematical Society in 1917, published the following year asAxiomatisches Denken (1918), he articulates his broadperspective on that method and presents it “at work” byconsidering, in detail, examples from various parts of mathematics andalso from physics. (Trees of branching type U) (dI-domains) << /S /GoTo /D (subsection.3.1.1) >> 734 0 obj endobj (The intuitionistic case) (The web of a coherence space) endobj << /S /GoTo /D (subsection.9.1.1) >> 476 0 obj endobj 552 0 obj 642 0 obj 526 0 obj endobj endobj 428 0 obj 354 0 obj 166 0 obj 342 0 obj << /S /GoTo /D (subsection.1.1.2) >> 214 0 obj 638 0 obj (Linearity) (Commuting conversions) 624 0 obj << /S /GoTo /D (section.14.1) >> endobj 482 0 obj 518 0 obj endobj << /S /GoTo /D (subsection.10.6.1) >> 338 0 obj 578 0 obj 256 0 obj (Linear Sequent Calculus) 138 0 obj 460 0 obj 646 0 obj (The theorem) << /S /GoTo /D (section.8.1) >> endobj 24 0 obj 352 0 obj 648 0 obj (Degree and conversion) (Structural rules) (Sums in Natural Deduction) 598 0 obj 726 0 obj 556 0 obj (Sum type) The proof, if you haven’t seen it before, is quite tricky but never-theless uses only standard ideas from the nineteenth century. endobj endobj << /S /GoTo /D (subsection.11.3.4) >> (Interpretation of F) endobj (Relevance of the isomorphism) << /S /GoTo /D (section.11.1) >> 562 0 obj << /S /GoTo /D (subsection.A.5.2) >> endobj 62 0 obj endobj 490 0 obj 502 0 obj 626 0 obj endobj endobj Proof theoretic ordinals 1.1 Preliminaries One of the aims of infinitary proof theory is the computation of the proof theoretical ordinal of axiom systems. endobj (Pairing) << /S /GoTo /D (subsection.A.2.1) >> 126 0 obj endobj (The algebraic tradition) (Coherence Spaces) << /S /GoTo /D (subsection.9.1.2) >> (Binary trees) (Atomic types) endobj endobj 140 0 obj 10 0 obj 720 0 obj >> 454 0 obj << /S /GoTo /D (subsection.5.1.5) >> 20 0 obj (The rules) endobj endobj 570 0 obj endobj 158 0 obj endobj endobj << /S /GoTo /D (section.12.2) >> 690 0 obj 618 0 obj endobj endobj endobj << /S /GoTo /D (section.B.5) >> endobj << /S /GoTo /D (subsection.5.1.1) >> << /S /GoTo /D (section.14.2) >> (Normalisation theorem) 248 0 obj << /S /GoTo /D (subsection.8.5.1) >> 496 0 obj (Semantics of System F) endobj endobj endobj (Subformula property) endobj << /S /GoTo /D (section.A.4) >> << /S /GoTo /D (section.10.5) >> endobj 152 0 obj 594 0 obj (Natural Numbers) endobj endobj (Interpretation) endobj endobj 34 0 obj endobj << /S /GoTo /D (subsection.3.1.2) >> 206 0 obj (Terms) endobj 286 0 obj 288 0 obj 442 0 obj endobj 520 0 obj endobj endobj endobj 170 0 obj endobj 588 0 obj << /S /GoTo /D (section.11.3) >> 28 0 obj 710 0 obj << /S /GoTo /D (chapter.9) >> (Definitions) 656 0 obj endobj 568 0 obj (Types) 622 0 obj 58 0 obj endobj endobj endobj endobj 730 0 obj (Integers) (The calculus) endobj endobj << /S /GoTo /D (subsection.11.5.3) >> (The Function-Space) endobj endobj 604 0 obj In evidence theory, likelihood is assigned to sets, as opposed to probability theory where likelihood is assigned to a probability density function. 580 0 obj 294 0 obj endobj 658 0 obj 504 0 obj endobj (Reducibility with parameters) endobj endobj 388 0 obj 634 0 obj endobj endobj (The Hauptsatz) (Sequent Calculus and Natural Deduction) endobj %PDF-1.2 << /S /GoTo /D (section.B.3) >> We will indicate in these lectures that there are different types of proof theoretical … << /S /GoTo /D (subsection.A.1.3) >> (Product type) 486 0 obj << /S /GoTo /D (subsection.15.1.3) >> 672 0 obj endobj endobj 616 0 obj << /S /GoTo /D (section.4.3) >> endobj 420 0 obj << /S /GoTo /D (section.8.3) >> 188 0 obj endobj endobj endobj 514 0 obj 632 0 obj endobj 76 0 obj endobj (Terms of universal type) (Properties of the interpretation) endobj 348 0 obj << /S /GoTo /D (subsection.14.2.3) >> endobj endobj 722 0 obj endobj 560 0 obj << /S /GoTo /D (subsection.12.3.2) >> endobj 116 0 obj endobj endobj endobj 636 0 obj endobj 282 0 obj (General ideas) PDF Infinitary Proof Theory - uni-muenster.de 1. 398 0 obj endobj (The Berry order) << /S /GoTo /D (section.3.3) >> 130 0 obj endobj (Stable functions) endobj 700 0 obj 290 0 obj (Some properties of the system without cut) endobj 724 0 obj endobj << /S /GoTo /D (subsection.A.3.2) >> << /S /GoTo /D (subsection.14.1.1) >> 668 0 obj 118 0 obj endobj (Representation of the constructors) endobj 72 0 obj endobj endobj endobj endobj >> endobj << /S /GoTo /D (subsection.A.1.1) >> 162 0 obj (Lambda Calculus) 182 0 obj (Numerals) endobj 120 0 obj endobj endobj (Total recursive functions) 52 0 obj 216 0 obj endobj 654 0 obj 208 0 obj endobj endobj 332 0 obj endobj x�}�_o� ���)x��2@(�j5��E�fكZ�f�Ku1~�Ak��҄.��ܔ�[. 714 0 obj << /S /GoTo /D (section.7.3) >> endobj endobj 474 0 obj endobj << /S /GoTo /D (section.11.5) >> 738 0 obj << 230 0 obj (Universal application) endobj (Reducibility) << /S /GoTo /D (subsection.5.2.1) >> 402 0 obj (Proofs into programs) 708 0 obj %PDF-1.5 472 0 obj 484 0 obj << /S /GoTo /D (section.8.2) >> 106 0 obj 466 0 obj << /S /GoTo /D (subsection.6.3.1) >> (Empty type) endobj endobj (Canonical forms) endobj << /S /GoTo /D (section.B.4) >> (The key cases) 306 0 obj 606 0 obj << /S /GoTo /D (subsection.7.4.1) >> endobj (The principal lemma) (Heyting) 458 0 obj 628 0 obj 236 0 obj endobj endobj 600 0 obj 274 0 obj 224 0 obj endobj endobj 202 0 obj (Of course) << /S /GoTo /D (subsection.11.5.4) >> << /S /GoTo /D (subsection.7.3.2) >> endobj 440 0 obj endobj << /S /GoTo /D (chapter.15) >> (System F) 296 0 obj endobj endobj endobj 220 0 obj (Coherence Spaces) 478 0 obj endobj endobj endobj << /S /GoTo /D (chapter.1) >> (Functoriality of arrow) 346 0 obj (Tokens for universal types) (Representation of provably total functions) endobj 322 0 obj 536 0 obj (The strong normalisation theorem) endobj endobj << /S /GoTo /D (subsection.10.3.2) >> %���� << /S /GoTo /D (section.13.2) >> endobj endobj endobj endobj (Natural Deduction) endobj << /S /GoTo /D (section.10.6) >> 376 0 obj 14 0 obj endobj << /S /GoTo /D (subsection.1.2.1) >> endobj << /S /GoTo /D (subsection.11.3.5) >> endobj endobj 36 0 obj (Properties of conversion) 686 0 obj (Representable functions) 540 0 obj 494 0 obj 278 0 obj << /S /GoTo /D (subsection.6.3.3) >> (Computational significance) << /S /GoTo /D (chapter.A) >> 238 0 obj 308 0 obj 508 0 obj 174 0 obj 380 0 obj endobj 644 0 obj (Partial functions) physicist must study the theory of his apparatus, and the philosopher criticizes reason itself.

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