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Abstract: We define well-partial-orderings on abstract algebras and give their order types. For every ordinal in an initial segment of Bachmann hierarchy there is one and only one (up to isomorphism) algebra giving the ordinal as order type. As a corollary, we show Kruskal-type theorems for various structures are equivalent to well-orderedness of certain ordinals. 1 Introduction The main theorem we prove in this paper is that the class of algebras yields a system of ordinal notations. Before making ... (Update)
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BibTeX entry: (Update)
@misc{ hasegawa-wellorderings,
author = "Ryu Hasegawa",
title = "Well-Orderings of Algebra and Kruskal's Theorem",
url = "citeseer.ist.psu.edu/hasegawa93wellorderings.html" }
Citations (may not include all citations):214 Orderings for term-rewriting systems (context) - Dershowitz - 1982
151 Proving termination with multiset orderings (context) - Dershowitz, Manna - 1979
108 Ordering by divisibility in abstract algebras (context) - Higman - 1952
51 Partially Ordered Algebraic Systems (context) - Fuchs - 1963
38 On well-quasi-ordering finite trees (context) - St, Nash-Williams - 1963
31 What's so special about Kruskal's theorem and the ordinal \G.. (context) - Gallier - 1991
24 Tree-width and well-quasiordering (context) - Robertson, Seymour et al. - 1990
23 Satisfiability of systems of ordinal notations with the subt.. (context) - Jouannaud, Okada
20 Attempts for generalizing the recursive path orderings (context) - Kamin, L'evy - 1980
19 Proof Theory of Impredicative Subsystems of Analysis (context) - Buchholz, Schutte - 1988
14 and Vazsonyi's conjecture (context) - Kruskal, the - 1960
14 Nonprovability of certain combinatorial properties of finite.. (context) - Simpson - 1985
11 Ordinal numbers and the Hilbert basis theorem (context) - Simpson - 1988
10 A constructive proof of Higman's lemma (context) - Murthy, Russell - 1990
9 A finite combinatorial principle which is equivalent to the .. (context) - Friedman, McAloon et al. - 1982
8 Reverse mathematics (context) - Simpson - 1985
7 Well-quasi-ordered sets (context) - Richman, Stolzenberg - 1993
7 Proof-theoretic investigations on Kruskal's theorem - Rathjen, Weiermann - 1993
4 A proof of Higman's lemma by structural induction - Coquand - 1993
4 Well-partial orderings and hierarchies (context) - de Jongh, Parikh - 1977
4 Proof theoretic techniques for term rewriting theory (context) - Dershowitz, Okada - 1988
4 Ordering structures and the Knuth-Bendix completion algorith.. (context) - Okada, Steel - 1988
3 A constructive proof that tree are well-quasi-ordered under .. (context) - Gupta - 1992
2 ordinals and termination (context) - Dershowitz - 1993
2 Ein in der reinen Zahlentheorie unbeweisbarer Satz uber endl.. (context) - Schutte, Simpson - 1985
1 the relation between choice and comprehension principles in .. (context) - Cantini - 1986
1 Uniform termination of term rewriting systems (context) - Lescanne - 1984
1 Konstruktiver Aufbau eines Abschnitts der zweiten Cantorsche.. (context) - Ackermann - 1951
1 An extension of Schutte's klammersymbols (context) - Gerber - 1967
1 Knuth-Bendix algorithm for Thue system based on kachinuki or.. (context) - Sakai - 1984
1 Two implementations of the recursive path ordering on monadi.. (context) - Lescanne - 1981
1 Preface: how we get from there to here (context) - Feferman - 1981
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