Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

The k-variable property is stronger than H-dimension k

Accepted versio

A logic road from special relativity to general relativity

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist

Dependence Logic with Generalized Quantifiers: Axiomatizations

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as "there exists uncountable many." Both of the axiomatizations are shown to be sound and complete for FO(Q) consequences.Comment: 17 page

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets

Complexity of equational theory of relational algebras with standard projection elements

The class $\mathsf{TPA}$ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $\mathsf{TPA}$ nor the first order theory of $\mathsf{TPA}$ are decidable. Moreover, we show that the set of all equations valid in $\mathsf{TPA}$ is exactly on the $\Pi ^1_1$ level. We consider the class $\mathsf{TPA}^-$ of the relation algebra reducts of $\mathsf{TPA}$’s, as well. We prove that the equational theory of $\mathsf{TPA}^-$ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work

Ronald V. Dellums v. George Bush (D.D.C. 1990): Memorandum Amicus Curiae of Law Professors

This joint memorandum is submitted to the court hearing Dellums v. Bush. This amicus brief advocates that the President may not order American armed forces to make war without consultation with and approval by Congress. The brief also argues that the case is justiciable

Evidence for protein-mediated fatty acid efflux by adipocytes

Abstract Aim: The hormonally controlled mobilization and release of fatty acids from adipocytes into the circulation is an important physiological process required for energy homeostasis. While uptake of fatty acids by adipocytes has been suggested to be predominantly protein-mediated, it is unclear whether the efflux of fatty acids also requires membrane proteins. Methods: We used fluorescent fatty acid efflux assays and colorimetric assays for free fatty acids and glycerol to identify inhibitors with effects on fatty acid efflux, but not lipolysis, in 3T3-L1 adipocytes. We assessed the effect of these inhibitors on a fibroblast-based cell line expressing fatty acid transport protein 1, hormone-sensitive lipase and perilipin, which presumably lacks adipocyte-specific proteins for fatty acid efflux. Results: We identified 4,4¢-diisothiocyanatostilbene-2,2¢-disulfonic acid (DIDS) as an inhibitor of fatty acid efflux that did not impair lipolysis or the cellular exit of glycerol but lead to an accumulation of intracellular fatty acids. In contrast, fatty acid efflux by the reconstituted cellular model for fatty acid efflux was responsive to lipolytic stimuli, but insensitive to DIDS inhibition. Conclusion: We propose that adipocytes specifically express an as yet unidentified DIDS-sensitive protein that enhances the efflux of fatty acids and therefore may lead to novel treatment approaches for obesity-related disorders characterized by abnormal lipid fluxes and ectopic triglyceride accumulation

\u3cem\u3eRonald V. Dellums v. George Bush\u3c/em\u3e (D.D.C. 1990): Memorandum \u3cem\u3eAmicus Curiae\u3c/em\u3e of Law Professors

This joint memorandum is submitted to the court hearing Dellums v. Bush. This amicus brief advocates that the President may not order American armed forces to make war without consultation with and approval by Congress. The brief also argues that the case is justiciable