Every Pointfree Funcoid on a Semilattice is an Algebraic Structure
Continuing this blog post: The set of all pointfree funcoids on upper semilattices with least elements is exactly a certain algebraic structure defined by propositional formulas. Really just add the identities defining a pointfree funcoid to the identities of an upper semilattice with least element. I will list the exact list of identities defining a […]
Funcoid is a “Structure” in the Sense of Math Logic
A few seconds ago I realized that certain cases of pointfree funcoids can be described as a structure in the sense of mathematical logic, that is as a finite set of operations and relational symbols. Precisely, if a pointfree funcoid $latex f$ is defined on a lattice (or semilattice) with a least element $latex \bot$, […]
My old files related with math logic
In 2005 year I put online some math articles related with formulas and math logic (despite I am not a professional logician). In 2005 I like a crackpot thought that I discovered a completely new math method replacing axiomatic method. This was a huge error (my skipped proof was just wrong). After that the files […]
How proof by contradiction differs of direct proof
This my post is about mathematical logic, but first I will explain the story about people who asked or answer this question. A famous mathematician Timoty Gowers asked this question: What is the difference between direct proofs and proofs by contradiction. We, people, are capable of doing irrational things and to be discouraged. I wrote […]
Formalistics of generalization
In the framework of ZF formally considered generalizations, such as whole numbers generalizing natural number, rational numbers generalizing whole numbers, real numbers generalizing rational numbers, complex numbers generalizing real numbers, etc. The formal consideration of this may be especially useful for computer proof assistants.