Scott V. Tezlaf

Scott V. Tezlaf

About

3
Publications
1,647
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Introduction
S. V. Tezlaf specializes in research of set theory, topology, mathematical physics. Current project: 'Foundations via a translinear calculus.'
Additional affiliations
July 2018 - present
StGIS
Position
  • Instructor
July 2015 - July 2018
Kumon Leysin Academy of Switzerland
Position
  • Instructor
November 2007 - September 2008
University of Massachusetts Amherst
Position
  • Laboratory Assistant
Education
August 2003 - June 2008

Publications

Publications (3)
Preprint
Full-text available
For over a century, the study of transfinite ordinal and cardinal values has grown into a vast body of compelling research into the logic of infinite quantities. However, one of the most central notions of the field has remained an open problem since the beginning. The continuum hypothesis, which attempts to define specific bounds on countable and...
Preprint
Here it is shown that by equipping nonordered sets of various dimensionality with a novel algebra, one can conveniently describe relationships that have been especially difficult to study—in particular, the mathematics of spinors, which underpin the physics of fermionic particles. In addition to a Clifford algebra, the described formalism produces...
Preprint
Full-text available
This paper explores properties and applications of an ordered subset of the quadratic integer ring $\mathbb{Z}[\frac{1+\sqrt{5}}{2}]$. The numbers are shown to exhibit a parity triplet, as opposed to the familiar even/odd doublet of the regular integers. Operations on these numbers are defined and used to generate a succinct recurrence relation for...

Projects

Project (1)
Project
The results of this research reveal surprising discoveries that bridge the fields of topology, set theory, calculus, number theory, projective geometry, logic, and the mathematics of spinors. Through a novel geometric argument on transfinite cardinalities, in addition to the equipping of non-ordered sets with a unique algebra, a multitude of exciting relations are uncovered, some of which are as follows: -An intuitive and fundamental representation of spinors. -A robust, algebraic derivation of differential calculus free from presumptions of limits and independent from the notion of infinitesimals. -A deep and meaningful cardinalization of topological elements, e.g., the topologies of the open, half-closed, and closed intervals are shown to identify with the values of 1/2, 1, and 3/2, respectively. -A meaningful quantification of transfinite cardinalities, e.g., aleph_0 is shown to be isomorphic to the quantity 1/2, represented topologically via the open interval previously stated. -An abelian alternative to linear algebra. -An inherent logic defined by the rational numbers. The mathematical results of this research have direct implications for the physical sciences, in particular, quantum field theory — demonstrated, for example, through its concise framework for describing spinors. A goal of this work is to establish a clear, logical justification for the quantum, i.e., stochastic, behavior of nature.