author={Robert Passmann},
  journal={The Journal of Symbolic Logic},
  • Robert Passmann
  • Published 1 December 2021
  • Philosophy, Computer Science
  • The Journal of Symbolic Logic
. We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of realisability with Beth semantics. On the way, we also show that the propositional admissible rules of CZF are exactly those of intuitionistic propositional logic. 

Logics and Admissible Rules of Constructive Set Theories

We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a

Lower Bounds on β ( α ) and other properties of α -register machines

. This paper extends our paper [C2] for the conference “Com-putability in Europe” 2022. After Infinite Time Turing Machines (ITTM) were introduced in Hamkins and Lewis [HL], a number of machine models



Logics of intuitionistic Kripke-Platek set theory

On the quantificational logic of intuitionistic set theory

Formal propositional logic describing the laws of constructive (intuitionistic) reasoning was first proposed in 1930 by Heyting. It is obtained from classical pro-positional calculus by deleting the

De Jongh's Theorem for Intuitionistic Zermelo-Fraenkel Set Theory

It is proved that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional Logic IPC and CZF has the de Jongh property with respect to every intermediate logic that is complete withrespect to a class of finite trees.

Realisability for Infinitary Intuitionistic Set Theory

We introduce a realisability semantics for infinitary intuitionistic set theory that employs Ordinal Turing Machines (OTMs) as realisers. We show that our notion of OTM-realisability is sound with

Rules and Arithmetics

  • A. Visser
  • Philosophy, Mathematics
    Notre Dame J. Formal Log.
  • 1999
A new theorem is proved: the admissible propositional rules of Heyting Arithmetic are the same as the admissive rules of Intuitionistic Propositional Logic, indicating the 'logical structure' of arithmetical theories.

On the admissible rules of intuitionistic propositional logic

A conjecture by de Jongh and Visser is proved and a proof system for the admissible rules of intuitionistic propositional logic is presented and semantic criteria for admissibility are given.

The Formulae-as-Classes Interpretation of Constructive Set Theory

The main objective of this paper is to show that a certain formulae-asclasses interpretation based on generalized set recursive functions provides a selfvalidating semantics for Constructive

Axiom of choice and complementation

It is shown that an intuitionistic model of set theory with the axiom of choice has to be a classical oneO A topos 6 is a category which has finite limits (i.e. finite products, intersections and a

A semantical proof of De Jongh's theorem

By a refinement of De Jongh's original method, a semantical proof is given of a result that is almost as good as Leivant's, and maximality of intuitionistic predicate calculus is established wrt.

A quasi-intumonistic set theory

It is shown that the consistency of the system the authors call IZF can be proved in the usual ZF set theory.