Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Finite, Feasible, Quantifier-free Foundation for Constructive Geometry   In this paper we will develop an axiomatic foundation for the geometric study
of straight edge, protractor, and compass constructions, which while being
related to previous foundations, will be the first to have all axioms written
and all proofs conducted in quantifier-free first order logic. All
constructions within the system will be justified to be feasible by basic human
faculties. No statement in the system will refer to infinitely many objects and
one can posit an interpretation of the system which is in accordance to our
free, creative process of geometric constructions. We are also able to capture
analogous results to Euclid's work on non-planar geometry in Book XI of The
Elements.
  This paper primarily builds on Suppes' paper Quantifier-Free Axioms for
Constructive Affine Plane Geometry and draws from Beeson's article A
Constructive Version of Tarski's Geometry. By further developing Suppes' work
on parallel line segments, we are able to develop analogs to most theorems
about parallel lines without assuming an equivalent to Euclid's Fifth Postulate
which we deem as introducing non-feasible constructions. In A Constructive
Version of Tarski's Geometry, Beeson defines the characteristics such a
geometric foundation should have to called constructive. This work satisfies
these characteristics. Additionally this work would be considered constructive
as Suppes defined it.

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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc