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Richard Zach

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Research and Publications

Projects

The Open Logic Project
The Collected Works of Rudolf Carnap
Paul Bernays: Philosopher of Mathematics

All papers

Papers by Subject

Click on links for abstracts, review information, and download links.

History of Logic

Carnap’s Early Metatheory: Scope and Limits
Heinrich Behmann’s 1921 lecture on the decision problem and the algebra of logic
The development of mathematical logic from Russell to Tarski
Kurt Gödel and computability theory
The practice of finitism: Epsilon calculus and consistency proofs in Hilbert’s Program
Hilbert’s “Verunglückter Beweis,” the first epsilon theorem, and consistency proofs
Completeness before Post: Bernays, Hilbert, and the development of propositional logic
Kurt Gödel, paper on the incompleteness theorems (1931)

Theory of Proofs

Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and any Other Truth-Functional Connective)
The epsilon calculus and Herbrand complexity
The epsilon calculus
Generalizing theorems in real closed fields
Note on generalizing theorems in algebraically closed fields
Short proofs of tautologies using the schema of equivalence
Algorithmic structuring of cut-free proofs

Philosophy of Mathematics

Hilbert’s program then and now
Gödel’s first incompleteness theorem and mathematical instrumentalism
Critical study of Michael Potter’s Reason’s Nearest Kin
Numbers and functions in Hilbert’s finitism
Hilbert’s Program
Hilbert’s Finitism. Historical, Philosophical, and Metamathematical Perspectives

Gödel Logics

First-order Gödel Logics
Characterization of the axiomatizable prenex fragments of first-order Gödel logics
Quantified propositional Gödel logic
Hypersequents and the proof theory of intuitionistic fuzzy logic
Compact propositional Gödel logics
Incompleteness of an infinite-valued first-order Gödel logic and of some temporal logics of programs

Finite-valued Logic

Labeled calculi and finite-valued logics
Approximating propositional calculi by finite-valued logics
Systematic construction of natural deduction systems for many-valued logics
Elimination of cuts in first-order many-valued logics
Proof Theory of Finite-Valued Logics

Other Logic

Effective Finite-Valued Approximations of General Propositional Logics
Decidability of quantified propositional intuitionistic logic and S4 on trees of height and arity ≤ ω
A complete first-order temporal logic of time with gaps
Tableaux for reasoning about atomic updates

Other Writings

Vagueness, Logic and Use: Four Experimental Studies on Vagueness

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Recent Posts

An Introduction to Proof Theory: Normalization, Cut-elimination, and Consistency Proofs
New details on why Tarski was reluctant to leave Poland before WWII
Updates to OLP for Fall 2021 edition of Sets, Logic, Computation
Famous logicians and their inconsistent theories
forall x: Calgary goes international (and other updates)

Recent Comments

Resumen de lecturas compartidas durante noviembre de 2020 | Vestigium on The significance of the Curry-Howard isomorphism
New details on why Tarski was reluctant to leave Poland before WWII – Richard Zach on Alfred Tarski: Life and Logic
Updates to OLP for Fall 2021 edition of Sets, Logic, Computation – Open Logic Project on Satisfaction and assignments
forall x: Calgary goes international (and other updates) – Open Logic Project on Adding online exercises with automated grading to any logic course with Carnap
Proof Theory of Finite-Valued Logics – Richard Zach on Systematic construction of natural deduction systems for many-valued logics

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