Isomorphism of index sets of discrete families of general recursive functions.
Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order
In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18].
Isomorphisms of Direct Products of Finite Commutative Groups
We have been working on the formalization of groups. In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative group which order is composite number is isomorphic to a direct product of finite commutative groups which orders are relatively prime. Next, we describe finite direct products of finite commutative groups
Isomorphisms of Direct Products of Finite Cyclic Groups
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.
Isotopy invariant quasigroup identities
According to S. Krstić, there are only four quadratic varieties which are closed under isotopy. We give a simple procedure generating quadratic identities and deciding which of the four varieties they define. There are about 37000 such identities with up to five variables.
It is consistent that there exists an ordered real closed field which is not hyper-real.
Iterated products of ideals of Borel sets
Iterated ultrapower and Prikry's forcing
Iterating along a Prikry sequence
We introduce a new method which combines Prikry forcing with an iteration between the Prikry points. Using our method we prove from large cardinals that it is consistent that the tree property holds at ℵₙ for n ≥ 2, is strong limit and .
Iteration of -complete forcing notions not collapsing .