We offer a view on how probability is related to logic. Specifically, we argue against the widely held belief that standard classical logics have no direct way of modelling the certainty of assumptions in theories and no direct way of stating the certainty of theorems proved from these (uncertain) assumptions. The argument rests on the observation that probability densities, being functions, ca...

I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are...

A theory is called κ-categorical, or categorical in power κ, if it has one model up to isomorphism of cardinality κ. Morley’s Categoricity Theorem states that if a theory of first order logic is categorical in some uncountable power κ, then it is categorical in every uncountable power. We provide an elementary exposition of this theorem, by showing that a theory is categorical in some uncountab...

We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are 2א1 pairwise non-isomorphic atomic models of T , each of size א1.

The Flexible Time-Triggered Switched Ethernet (FTT-SE) protocol was proposed in 2006 [1] as a realization of the FTT paradigm [2] specifically adapted to switched Ethernet. This paradigm first appeared in 1998 implemented on CAN, the FTT-CAN protocol [3], followed by an implementation on shared Ethernet in 2002 [4]. The FTT paradigm is a framework to develop distributed real-time systems that a...

Solving equations is one of the main themes in mathematics. A large part of the combinatorial group theory revolves around the word and conjugacy problems particular types of equations in groups. Whether a given equation has a solution in a given group is, as a rule, a non-trivial problem. A more general and more difficult problem is to decide which formulas of the first-order logic hold in a g...

It is shown that the positive first-order theory of an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J , we show that the positive first-order theory of G can be reduced to the existential first-order theory of G in case ...

OBJECTIVE Outcomes of the supraclavicular artery island flap (SCAIF) have not been extensively studied in comparison with free tissue transfer (FTT) flaps for head and neck reconstruction. We hypothesize that the pedicled SCAIF has decreased operating room time, length of stay, time to wound healing of recipient site, complications, and hospital charges as compared with FTT. STUDY DESIGN Case...