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Axiomatic Theory of Formulas - Links

Axiomatic Theory of Formulas (ATF which also may stand for algebraic theory of formulas) was discovered by me, Victor Porton in 2005 year.

See also: my math logic research (because the algebraic theory of formulas is a new foundation for algebraic logic) and theory of dependencies.

This new theory is a new foundation for math logic, that is foundation of the foundations of mathematics. I advise to add this new theory to the University program.

Here is the list of formulas theory Web pages on this site:

Operator Theory of Formulas - online math article

• Part 1: Axiomatic Theory of Formulas - an abstract axiomatic (algebraic) theory of mathematical formulas, as well as of any mathematical objects which have indexed parts of different kinds.
• Part 2: Representation Related Properties of Formulas - properties of formulas related with representation as well as some more sophisticated properties of formulas, also applying operators to parts (subformulas) of formulas, such as substitutions.

Algebraic Theory of Formulas (requires a MathML supporting browser to view)

It is a newer version (unfinished draft) of the theory, with many significant changes and enhancements. (XML source made with XSLT Math)

This version of the article consists of the following parts:

Theory of Dependencies (see also main theory of dependencies page)

Entire dependencies article as one page By parts:

• Objects and Classes (Multi-dimensional Relations). Classes with Argument and Result (Dependencies)
• Category of Dependencies
  • Main Theorem about Category of Dependencies
• Category of Dependencies - Relations Between Elements

My newer generalizations of the theory of dependencies

• Category of endomorphisms and pseudomorphisms - my new generalization of the theory of dependencies as a category induced by an arbitrary category with partially ordered morphisms.
• Theory of Dependencies (rough draft) - new version of dependencies theory article.
• Axiomatic theory of dependencies (partial draft) - my earlier (not quite successful) attempt to reformulate the theory of dependencies for general case of semigroups.

Theory of Constructs (Dependencies with Parameter)

Entire Systems of Constructs article as one page By parts:

• Definition of Systems of Constructs
• Repeatedly Applied Dependencies (Relations with Parameters)
• Disjunctive Pseudomorphisms (an important specific case of pseudomorphisms)
• Factor of Two Constructs (function which transforms one formula to an other)

Theory of Formulas Itself

• (not yet written)

More

New definition of factor of constructs (rough unfinished draft)

It will eventually replace the old definition. The new definition is more algebraic and more functional.

Research plans for theory of formulas

Immediate research plans for theory of dependencies, theory of constructs, and theory of formulas.

Different Viewpoints on Axiomatic Theory of Formulas

An informal overview of relations of the axiomatic theory of formulas with different fields of mathematics and with philosophy.

Related Links

On this site

• Theory of dependencies (algebra of categories)
• My math logic research
• Theory of formulas in my math weblog
• Journal of post-Axiomatic Mathematics and Logic.
• My weblog message about formulas expressed as triples being a very fascinating thing.

Other sites

• Mathematical Logic around the world
• Science > Math > Logic and Foundations (ODP Web directory)
  • Science > Math > Logic and Foundations > Foundations
  • Science > Math > Logic and Foundations > Model Theory
• Computers > Algorithms > Computational Algebra (ODP Web directory)
• Computers > Computer Science > Theoretical (ODP Web directory)
• Formula and Expression at 3Apes Web directory

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