On the consistency of a slight (?) Modification of quine'sMew Foundations

  title={On the consistency of a slight (?) Modification of quine'sMew Foundations},
  author={Ronald B. Jensen},
Foundations of applied mathematics I
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 (withExpand
Rank-initial embeddings of non-standard models of set theory
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
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 ‘TranscendentalExpand
Executing Gödel’s programme in set theory
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 leastExpand
Feferman’s Forays into the Foundations of Category Theory
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 beExpand
Consistency of strictly impredicative NF and a little more …
  • Sergei Tupailo
  • 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
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 beenExpand
Automorphisms of models of bounded arithmetic
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¢0Expand
Logic Colloquium 2005: Monotone inductive definitions and consistency of New Foundations
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
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