Applying Set Theory E88

We prove some results in set theory as applied to general topology and model theory. In particular, we study ℵ1-collectionwise Hausdorff, Chang Conjecture for logics with Malitz-Magidor quantifiers and monadic logic of the real line by odd/even Cantor sets.

Monadic Bounded Algebras

<p>The object of study of the thesis is the notion of monadic bounded algebras (shortly, MBA's). These algebras are motivated by certain natural constructions in free (first-order) monadic logic and are related to free monadic logic in the same way as monadic algebras of P. Halmos to monadic logic (Chapter 1). Although MBA's come from logic, the present work is in algebra. Another important way of approaching MBA's is via bounded graphs, namely, the complex algebra of a bounded graph is an MBA and vice versa. The main results of Chapter 2 are two representation theorems: 1) every model is a basic MBA and every basic MBA is isomorphic to a model; 2) every MBA is isomorphic to a subdirect product of basic MBA's. As a consequence, every MBA is isomorphic to a subdirect product of models. This result is thought of as an algebraic version of semantical completeness theorem for free monadic logic. Chapter 3 entirely deals with MBA-varieties. It is proved by the method of filtration that every MBA-variety is generated by its finite special members. Using connections in terms of bounded morphisms among certain bounded graphs, it is shown that every MBA-variety is generated by at most three special (not necessarily finite) MBA's. After that each MBA-variety is equationally characterized. Chapter 4 considers finitely generated MBA's. We prove that every finitely generated MBA is finite (an upper bound on the number of elements is provided) and that the number of elements of a free MBA on a finite set achieves its upper bound. Lastly, a procedure for constructing a free MBA on any finite set is given.</p>

Monadic Bounded Algebras

<p>The object of study of the thesis is the notion of monadic bounded algebras (shortly, MBA's). These algebras are motivated by certain natural constructions in free (first-order) monadic logic and are related to free monadic logic in the same way as monadic algebras of P. Halmos to monadic logic (Chapter 1). Although MBA's come from logic, the present work is in algebra. Another important way of approaching MBA's is via bounded graphs, namely, the complex algebra of a bounded graph is an MBA and vice versa. The main results of Chapter 2 are two representation theorems: 1) every model is a basic MBA and every basic MBA is isomorphic to a model; 2) every MBA is isomorphic to a subdirect product of basic MBA's. As a consequence, every MBA is isomorphic to a subdirect product of models. This result is thought of as an algebraic version of semantical completeness theorem for free monadic logic. Chapter 3 entirely deals with MBA-varieties. It is proved by the method of filtration that every MBA-variety is generated by its finite special members. Using connections in terms of bounded morphisms among certain bounded graphs, it is shown that every MBA-variety is generated by at most three special (not necessarily finite) MBA's. After that each MBA-variety is equationally characterized. Chapter 4 considers finitely generated MBA's. We prove that every finitely generated MBA is finite (an upper bound on the number of elements is provided) and that the number of elements of a free MBA on a finite set achieves its upper bound. Lastly, a procedure for constructing a free MBA on any finite set is given.</p>

Merleau-Ponty on the Sexed Body

This paper engages with Maurice Merleau-Ponty’s account of the sexed body in the Phenomenology of Perception. I focus on his notion of the sexual schema to show that, contrary to a number of feminist critiques, it does not (1) posit a neutral body overcoded by culturally-contingent sexual determinations or (2) erase the feminine body, but is informed by Merleau-Ponty particular version of the phenomenological reduction whereby factic determinations are “bracketed” to permit the object under study to reveal itself as it is rather than as we wish it to be or have been conditioned to think it. I subsequently defend Merleau-Ponty against the long-standing claim that entwining sexuality with existence prevents an analytic and by extension positive conception of sexuality by arguing that he rejects the monadic logic that this charge is premised on to instead challenge us to think of sexuality in terms of its integration with an individual’s entire embodied, embedded existence. The result is an analysis that emphasizes the ambiguity, afoundationalism, individuality, and open-ended immanent expressivity of sexuality.

Revisiting separation: algorithms and complexity

Linear temporal logic (LTL) with Since and Until modalities is expressively equivalent, over the class of complete linear orders, to a fragment of first-order logic known as FOMLO (first-order monadic logic of order). It turns out that LTL, under some basic assumptions, is expressively complete if and only if it has the property, called separation, that every formula is equivalent to a Boolean combination of formulas that each refer only to the past, present or future. Herein we present simple algorithms and their implementations to perform separation of the LTL with Since and Until, over discrete and complete linear orders, and translation from FOMLO formulas into equivalent temporal logic formulas. We additionally show that the separation of a certain fragment of LTL results in at most a double exponential size growth.

Political Competition and the Initiation of International Conflict

Although some scholars claim that the empirical evidence for the very low instance of interstate war between democracies is well established, others have raised new challenges. But even if democratic peace is observed, its theoretical explanation remains unresolved. Consensus has not emerged among competing approaches, some of which are criticized for offering monadic logic for a dyadic phenomenon. This article synthesizes recent literature to advance a simple, but distinct, explicitly dyadic theory about institutionalized political competition, leading to expectations that it is the most important source of democratic peace. While the authors are far from the first to consider political competition, their approach stands out in according it the central role in a dyadic theory focused on the regime type of initiators and target states. They argue that potential vulnerability to opposition criticism on target-regime-specific normative and costs-of-war bases is more fundamental than mechanisms such as audience costs, informational effects, or public goods logic. Incumbents in high-competition states will be reluctant to initiate conflict with a democracy due to anticipated inability to defend the conflict as right, necessary, and winnable. The authors present new and highly robust evidence that democratic peace is neither spurious nor a methodological artifact, and that it can be attributed to high-competition states’ aversion to initiating fights with democracies.