8 citations · 17 across the 19 of their papers we have counts for
26 papers
What David Teaches Goliath: An Inevitable Extension of ZFC
Ali Enayat
We examine the metamathematical significance of the Levy scheme , which asserts, for each natural number , the existence of an -Mahlo cardinal such that $V_κ\prec_{Σ_n…
Mathematics in the age of the reproduction of intelligence
Ali Enayat
Drawing on Walter Benjamin's account of technological reproducibility and aura in relation to art, together with insights from Yehuda Rav and Ludwig Wittgenstein, this speculative…
Tarskian truth theories over set theory
Ali Enayat
This work uses mostly model-theoretic methods to establish new proof-theoretic theorems about several axiomatic theories of truth over KP (Kripke-Platek set theory) and stronger th…
Corrigendum & Addendum to "Categoricity-like Properties in the First Order Realm"
Ali Enayat, Mateusz Łełyk
This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
Corrigendum & Addendum to: Variations on a Visserian theme
Ali Enayat
We revisit the proof of solidity of KM (Kelley-Morse theory of classes), as presented in the 2016 paper "Variations on a Visserian theme", so as to indicate the role of the scheme…
The Mostowski Bridge
Ali Enayat
In 1950, Novak and Mostowski showed that GB (Gödel-Bernays theory of classes) is conservative over ZF, and therefore by Gödel's second incompleteness theorem the consistency of ZF…
Models of Set Theory: Extensions and Dead-ends
Ali Enayat
This paper is a contribution to the study of extensions of arbitrary models of ZF (Zermelo-Fraenkel set theory), with no regard to countability or well-foundedness of the models in…
Incompleteness of boundedly axiomatizable theories
Ali Enayat, Albert Visser
Our main result (Theorem A) shows the incompleteness of any consistent sequential theory T formulated in a finite language such that T is axiomatized by a collection of sentences o…
Satisfaction classes with approximate disjunctive correctness
Ali Enayat
We present two new constructions of satisfaction/truth classes over models of PA (Peano Arithmetic) that provide a foil to the fact that the existence of a disjunctively correct fu…
Indiscernibles and satisfaction classes in arithmetic
Ali Enayat
We investigate the theory PAI (Peano Arithmetic with Indiscernibles). Models of PAI are of the form (M, I), where M is a model of PA, I is an unbounded set of order indiscernibles…
End extending models of set theory via power admissible covers
Zachiri McKenzie, Ali Enayat
Motivated by problems involving end extensions of models of set theory, we develop the rudiments of the power admissible cover construction (over ill-founded models of set theory),…
Set theory with a proper class of indiscernibles
Ali Enayat
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe. One of the main results…
An unpublished theorem of Solovay, revisited
Ali Enayat, Vladimir Kanovei
A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and -large generic extensions of the constructible universe .
Set theoretical analogues of the Barwise-Schlipf theorem
Ali Enayat
We characterize nonstandard models of ZF (of arbitrary cardinality) that can be expanded to Goedel-Bernays class theory plus -Comprehension. We also characterize countable n…
The Barwise-Schlipf Theorem
Ali Enayat, James H. Schmerl
In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model of PA (Peano arithmetic) is recursively saturated iff $\mat…
Condensable models of set theory
Ali Enayat
We study models M of set theory that are "condensable", in the sense that there is an "ordinal" v of M such that the rank initial segment of M determined by v is both isomorphic to…
Initial self-embeddings of models of set theory
Ali Enayat, Zachiri McKenzie
By a classical theorem of Harvey Friedman (1973), every countable nonstandard model of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding $…
Truth and Feasible Reducibility
Ali Enayat, Mateusz Łełyk, Bartosz Wcisło
Let be any of the three canonical truth theories (Compositional truth without extra induction), (Friedman--Sheard truth without extra…
Topological models of arithmetic
Ali Enayat, Joel David Hamkins, Bartosz Wcisło
Ali Enayat had asked whether there is a nonstandard model of Peano arithmetic (PA) that can be represented as , where and $\otimes…
Truth, Disjunction, and Induction
Ali Enayat, Fedor Pakhomov
By a well-known result of Kotlarski, Krajewski, and Lachlan (1981), first-order Peano arithmetic can be conservatively extended to the theory of a truth predicate…
Fixed Points of Self-embeddings of Models of Arithmetic
Saeideh Bahrami, Ali Enayat
We investigate the structure of fixed point sets of self-embeddings of models of arithmetic. In particular, given a countable nonstandard model M of a modest fragment of Peano arit…
Variations on a Visserian Theme
Ali Enayat
A first order theory T is said to be "tight" if for any two deductively closed extensions U and V of T (both of which are formulated in the language of T), U and V are bi-interpret…
Iterated Ultrapowers for the Masses
Ali Enayat, Matt Kaufmann, Zachiri McKenzie
We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indisc…
ZFC proves that the class of ordinals is not weakly compact for definable classes
Ali Enayat, Joel David Hamkins
We prove that the class of all ordinals Ord is not weakly compact with respect to definable classes. Specifically, in any model of ZFC, the definable tree property fails for Ord, i…