26 citations · 35 across the 32 of their papers we have counts for
16 papers · 2 filters
The Largest Suslin Axiom
Grigor Sargsyan, Nam Trang
We develop the basic fine structure theory of the minimal model of the Largest Suslin Axiom. In particular, we prove that that the minimal model of the Largest Suslin Axiom satisfi…
On the derived models of self iterable universes
Grigor Sargsyan, Takehiko Gappo
We show that if the universe is self-iterable and is an inaccessible limit of Woodin cardinal then is regular" holds in the derived model at . The proof is fine-…
Hod up to AD is measurable
Grigor Sargsyan, Rachid Atmai
Suppose is a transitive class size model of is regular". is a minimal model of is measurable" if (i) $\mathbb{R}, Ord\subseteq M…
Ideals and Strong Axioms of Determinacy
Dominik Adolf, Grigor Sargsyan, Nam Trang +2
We show that the following two theories are equiconsistent: (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal such that if j is the generic embedding associ…
An inner model theoretic proof of Becker's theorem
Grigor Sargsyan
We give a new proof of a theorem of Becker that under AD+V=L(R), omega_2 is a kappa-supercompact for every kappa less than or equal to the supremum of all Suslin cardinals. Our pro…
Sealing from Iterability
Grigor Sargsyan, Nam Trang
We obtain sealing by forcing over a self-iterable model. The proof is fine-structure free and uses only basic ideas from iteration theory. We believe that such fine-structure free…
Translation procedures in descriptive inner model theory
Grigor Sargsyan
We develop a basic translation procedure that translates a hod mouse to an equivalent mouse. Unlike the translation procedure used by Steel and Zhu, our procedure works in a coarse…
The mouse set conjecture for sets of reals
Grigor Sargsyan, John Steel
Recall that the Mouse Set Conjecture says that under AD++V=L(P(R)), a real is ordinal definable if and only if it belongs to an iterable mouse. The Mouse Set Conjecture for sets of…
implies that all sets of reals are universally Baire
Grigor Sargsyan
is the Axiom of Determinacy for games on the reals (i.e., the player play reals. We show that it implies that all sets of reals are Theta-universally Baire. As a…
Covering with Chang models over derived models
Grigor Sargsyan
We present a covering conjecture that we expect to be true below superstrong cardinals. We then show that the conjecture is true in hod mice. This work is a continuation of the wor…
A characterization of extenders of HOD
Grigor Sargsyan
Assume . Let , the supremum of all prewellorderings. We prove that extenders on the sequence of $\H$ that have critical point …
Varsovian models II
Grigor Sargsyan, Ralf Schindler, Farmer Schlutzenberg
Assume the existence of sufficent large cardinals. Let be the minimal iterable proper class model satisfying "there are s…
Negative results on precipitous ideals on omega_1
Grigor Sargsyan
We show that in extender models there are no generic embeddings with critical point that resemble the stationary tower at the second Woodin cardinal.
The exact strength of generic absoluteness for the universally Baire sets
Grigor Sargsyan, Nam Trang
A set of reals is \textit{universally Baire} if all of its continuous preimages in topological spaces have the Baire property. is a type of generic absoluteness cond…
Hjorth's reflection argument
Grigor Sargsyan
Hjorth, assuming , showed that there is no sequence of length consisting of distinct -sets. We show that the same theory implies that for , t…
Failures of square in Pmax extensions of Chang models
Paul B. Larson, Grigor Sargsyan
We show that the statements and both fail in the extension of a variation of the Chang model introduced by Sargsyan.