4 citations · 12 across the 17 of their papers we have counts for
8 papers · 1 filter
On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC
Amitayu Banerjee, Alexa Gopaulsingh, Zalán Molnár
In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs int…
On Erdos--Dushnik--Miller theorem without AC
Amitayu Banerjee, Alexa Gopaulsingh
In set theory without the Axiom of Choice, we study the possible placement of Erdos-Dushnik-Miller theorem restricted to an uncountable set of vertices in the hierarchy of weak cho…
Partition models, Permutations of infinite sets without fixed points, and weak forms of AC
Amitayu Banerjee
We study new relations of the following statements with weak choice principles in ZF and ZFA. 1. There does not exist an infinite Hausdorff space X such that every infinite subset…
Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC
Amitayu Banerjee
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements with weak choice principles. 1. Every locally finite connected graph has a maxi…
On some applications of strongly compact Prikry forcing
Amitayu Banerjee
We work with symmetric inner models of forcing extensions based on strongly compact Prikry forcing to extend some known results.
Chromatic number of the product of graphs, graph homomorphisms, Antichains and cofinal subsets of posets without AC
Amitayu Banerjee, Zalán Gyenis
We have observations concerning the set theoretic strength of the following combinatorial statements without the axiom of choice. 1. If in a partially ordered set, all chains are f…
Combinatorial Properties and Dependent choice in symmetric extensions based on Lévy Collapse
Amitayu Banerjee
We work with symmetric extensions based on Lévy Collapse and extend a few results of Arthur Apter. We prove a conjecture of Ioanna Dimitriou from her P.h.d. thesis. We also observe…
First order logic without equality on relativized semantics
Amitayu Banerjee, Mohamed Khaled
Let be any ordinal. We consider the class of relativized diagonal free set algebras of dimension . With same technique, we prove several important res…