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A fixed point theory over stratified truth
Author(s) -
Cantini Andrea
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201900064
Subject(s) - mathematics , stratification (seeds) , monotone polygon , quine , fixed point , set theory , discrete mathematics , calculus (dental) , pure mathematics , epistemology , computer science , mathematical analysis , set (abstract data type) , philosophy , geometry , medicine , seed dormancy , botany , germination , dentistry , dormancy , biology , programming language
We present a theory of stratified truth ST μ with a μ‐operator, where terms representing fixed points of stratified monotone operations are available. We prove that ST μ is relatively intepretable into Quine's NF (or subsystems thereof). The motivation is to investigate a strong theory of truth, which is consistent by means of stratification , i.e., by adopting an implicit type theoretic discipline, and yet is compatible with self‐reference (to a certain extent). The present version of ST μ is an enhancement of the theory presented in [2].