Reverse Bridge Theorem under Constraint Partition

A Partition Theorem

We prove a partition theorem (in the sense of the theorems of Ramsey [3], Erdös-Rado [1], and Rado [2]) which together with a forthcoming paper by Halpern and A. Levy will constitute a proof of the independence of the axiom of choice from the Boolean prime ideal theorem in Zermelo-Fraenkel set theory with the axiom of regularity. Although the theorem arises in logic, it is of a purely combinato...

Euler's Partition Theorem

Euler’s Partition Theorem states that the number of partitions with only distinct parts is equal to the number of partitions with only odd parts. The combinatorial proof follows John Harrison’s pre-existing HOL Light formalization [1]. To understand the rough idea of the proof, I read the lecture notes of the MIT course 18.312 on Algebraic Combinatorics [2] by Gregg Musiker. This theorem is the...

A Partition Theorem

We deal with some relatives of the Hales Jewett theorem with primitive recursive bounds.

A Partition Theorem for [0,1]

We prove a Hindman-type partition theorem for Baire partitions of [0, 1].

Quantum Reverse Shannon Theorem