Thesis (Ph. D.)--Oregon State University, 1990. / Typescript (photocopy). Includes bibliography (leaf 42). Also available on the World Wide Web.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 276-279).

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 46-47).

Paper 1. This paper establishes several algebraic embedding theorems, each of which asserts that a certain kind of residuated structure can be embedded into a richer one. In almost all cases, the original structure has a compatible involution, which must be preserved by the embedding. The results, in conjunction with previous findings, yield separative axiomatizations of the deducibility relations of various substructural formal systems having double negation and contraposition axioms. The separation theorems go somewhat further than earlier ones in the literature, which either treated fewer subsignatures or focussed on the conservation of theorems only. Paper 2. It is proved that the variety of relevant disjunction lattices has the finite embeddability property (FEP). It follows that Avron’s relevance logic RMImin has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron’s result that RMImin is decidable. Paper 3. An idempotent residuated po-monoid is semiconic if it is a subdirect product of algebras in which the monoid identity t is comparable with all other elements. It is proved that the quasivariety SCIP of all semiconic idempotent commutative residuated po-monoids is locally finite. The lattice-ordered members of this class form a variety SCIL, which is not locally finite, but it is proved that SCIL has the FEP. More generally, for every relative subvariety K of SCIP, the lattice-ordered members of K have the FEP. This gives a unified explanation of the strong finite model property for a range of logical systems. It is also proved that SCIL has continuously many semisimple subvarieties, and that the involutive algebras in SCIL are subdirect products of chains. Paper 4. Anderson and Belnap’s implicational system RMO can be extended conservatively by the usual axioms for fusion and for the Ackermann truth constant t. The resulting system RMO is algebraized by the quasivariety IP of all idempotent commutative residuated po-monoids. Thus, the axiomatic extensions of RMO are in one-to-one correspondence with the relative subvarieties of IP. It is proved here that a relative subvariety of IP consists of semiconic algebras if and only if it satisfies x (x t) x. Since the semiconic algebras in IP are locally finite, it follows that when an axiomatic extension of RMO has ((p t) p) p among its theorems, then it is locally tabular. In particular, such an extension is strongly decidable, provided that it is finitely axiomatized. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2008.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (pages 42-44).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Embeddings; graph theory; pseudo-triangulations. Includes bibliographical references (leaves 30-31).

Sung Wing-wah. / Bibliography: leaves 42-45 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

Chen, Yunxia. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 54-56). / Abstracts in English and Chinese. / Chapter 1 --- Embedding in Hermitian case --- p.8 / Chapter 1.1 --- Basics on Riemannian symmetric spaces --- p.8 / Chapter 1.2 --- Embedding in Hermitian case --- p.11 / Chapter 1.2.1 --- Borel embedding theorem --- p.11 / Chapter 1.2.2 --- Harish-Chandra embedding theorem --- p.12 / Chapter 1.2.3 --- Hermann convexity theorem --- p.14 / Chapter 2 --- Embedding in generalized Grassmannian case --- p.15 / Chapter 2.1 --- Compact symmetric spaces as Grassmannians --- p.15 / Chapter 2.1.1 --- Preliminaries --- p.15 / Chapter 2.1.2 --- "Grassmannians, Lagrangian Grassmannians and Double Lagrangian Grassmannians" --- p.16 / Chapter 2.1.3 --- Compact simple Lie groups --- p.20 / Chapter 2.2 --- Embedding in generalized Grassmannian case --- p.23 / Chapter 2.2.1 --- Space-like Grassmannian --- p.23 / Chapter 2.2.2 --- Graph-like Grassmannian --- p.26 / Chapter 2.2.3 --- Convexity property --- p.27 / Chapter 3 --- Cut locus of Compact symmetric spaces --- p.29 / Chapter 3.1 --- Cut locus --- p.29 / Chapter 3.1.1 --- Cut locus of Riemannian manifold --- p.29 / Chapter 3.1.2 --- Lie algebra of compact symmetric space --- p.31 / Chapter 3.1.3 --- Tangent cut locus of compact symmetric spaces --- p.32 / Chapter 3.2 --- Hermitian case and generalized Grassmannian case --- p.36 / Chapter 3.2.1 --- The Hermitian case --- p.36 / Chapter 3.2.2 --- The generalized Grassmannian case --- p.38 / Chapter 4 --- Construction of the explicit embedding --- p.42 / Chapter 4.1 --- Regular symmetric spaces --- p.42 / Chapter 4.2 --- Embedding in Regular case --- p.45 / Chapter 4.2.1 --- Construction of the embedding --- p.45 / Chapter 4.2.2 --- The properties of the explicit embedding --- p.47 / Chapter 4.3 --- Generalization of the embedding --- p.51 / Bibliography --- p.54