#### 11 Citations

Foundations of applied mathematics I

- Synthese
- 2021

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: $$ \mathsf {ZFCA}_{\sigma }$$ ZFCA σ (Zermelo–Fraenkel set theory (with… Expand

Rank-initial embeddings of non-standard models of set theory

- Mathematics, Computer Science
- Arch. Math. Log.
- 2020

Back-and-forth constructions are carried out to establish various generalizations and refinements of Friedman’s theorem on the existence of rank-initial embeddings between countable non-standard models of the fragment. Expand

God, Hypostasis, and the Threat of Paradox: Exploring Kantian And Non-Kantian Reasons for Circumspection

- Philosophy
- Kant Yearbook
- 2018

Abstract In this paper, I present an interpretation of Kant’s view that reason’s hypostasis of the idea of a sum-total of reality is dogmatic and illegitimate. In the section on the ‘Transcendental… Expand

Executing Gödel’s programme in set theory

- Mathematics
- 2017

The study of set theory (a mathematical theory of infinite collections) has garnered
a great deal of philosophical interest since its development. There are several reasons
for this, not least… Expand

Feferman’s Forays into the Foundations of Category Theory

- Mathematics
- 2017

This paper is primarily concerned with assessing a set-theoretical system, \(S^*\), for the foundations of category theory suggested by Solomon Feferman. \(S^*\) is an extension of NFU, and may be… Expand

Consistency of strictly impredicative NF and a little more …

- Computer Science, Mathematics
- The Journal of Symbolic Logic
- 2010

Using the technology of forcing, it is proved that the fragment of NF based on strictly impredicative Stratified Comprehension is consistent, and this is a new subsystem of NF shown to be consistent. Expand

A Revision Theoretic Model for NF

- 2008

Ever since Quine introduced his new set theory, New Foundations (NF), in the thirties, it has been unknown whether it is consistent relative to ZF. Efforts to find a model for it in ZF have been… Expand

Automorphisms of models of bounded arithmetic

- Mathematics
- 2006

We establish the following model theoretic characterization of the fragment I¢0+Exp+B§1 of Peano arithmetic in terms of fixed points of automorphisms of models of bounded arithmetic (the fragment I¢0… Expand

Logic Colloquium 2005: Monotone inductive definitions and consistency of New Foundations

- Mathematics
- 2005

In this paper we reduce the consistency problem for NF to consistency of a certain extension of Jensen’s NFU. Working in NFU+Pairing, which is known to be consistent relative to Zermelo set theory,… Expand

The Watson Theorem Prover

- Mathematics, Computer Science
- Journal of Automated Reasoning
- 2004

The mathematical foundations of the prover and the way these are presented to a user are discussed, and the development of automated proof strategies are allowed in the same way as theorems. Expand