# THE FIRST-ORDER LOGIC OF CZF IS INTUITIONISTIC FIRST-ORDER LOGIC

@article{Passmann2021THEFL, title={THE FIRST-ORDER LOGIC OF CZF IS INTUITIONISTIC FIRST-ORDER LOGIC}, author={Robert Passmann}, journal={The Journal of Symbolic Logic}, year={2021} }

. 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.

## 2 Citations

### Logics and Admissible Rules of Constructive Set Theories

- Mathematics
- 2022

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

- Mathematics
- 2023

. 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…

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