Related papers: Doubly partially conservative sentences
We study the status of preservation theorems such as the {\L}o\'s-Tarski theorem and the homomorphism preservation theorem in the context of semiring semantics. Semiring semantics has its origins in the provenance analysis of database…
We prove that in a theory $T$ stable over a predicate $P$, for any $\lambda > |T|$, there is a $\lambda$-prime model over any complete set A with a $\lambda$-saturated $P$-part.
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…
Let $\mathcal{PL}({\sf T},{\sf T}')$ and $\mathcal{PL}_{\Sigma_1}({\sf T},{\sf T}')$ respectively indicates the provability logic and $\Sigma_1$-provability logic of ${\sf T}$ relative in ${\sf T}'$. In this paper we characterize the…
The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…
Let T be an algebraically bounded theory. We consider the $L(\bar\delta)$-expansions of T by a tuple $\bar \delta$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose…
If kappa is strongly compact, lambda > kappa is regular, then (2^{< lambda})^+ --> (lambda+eta)^2_theta holds for eta,theta<kappa.
The higher-derivative $\alpha'$ corrections consistent with $O(d,d)$ duality invariance can be completely classified for cosmological, purely time-dependent backgrounds. This result is used to show that there are duality invariant theories…
Lexical Semantic Change is the study of how the meaning of words evolves through time. Another related question is whether and how lexical relations over pairs of words, such as synonymy, change over time. There are currently two competing,…
We prove preservation theorems for $\mathcal{L}_{\omega_1, G}$, the countable fragment of Vaught's closed game logic. These are direct generalizations of the theorems of \L{}o\'s-Tarski (resp. Lyndon) on sentences of $\mathcal{L}_{\omega_1,…
A pseudo-primitive word with respect to an antimorphic involution \theta is a word which cannot be written as a catenation of occurrences of a strictly shorter word t and \theta(t). Properties of pseudo-primitive words are investigated in…
The main result is that for lambda strong limit singular failing the continuum hypothesis (i.e. 2^lambda > lambda^+), a polarized partition theorem holds.
Contrastive learning has recently achieved compelling performance in unsupervised sentence representation. As an essential element, data augmentation protocols, however, have not been well explored. The pioneering work SimCSE resorting to a…
We investigate the problem of when $\leq\lambda$--support iterations of $<\lambda$--complete notions of forcing preserve $\lambda^+$. We isolate a property -- {\em properness over diamonds} -- that implies $\lambda^+$ is preserved and show…
We consider the related notions of two-prover and of relativistic commitment schemes. In recent work, Lunghi et al. proposed a new relativistic commitment scheme with a multi-round sustain phase that enables to keep the binding property…
The classical condition "$\phi$ is a semantic consequence of $\Theta$" in infinite-valued propositional \L ukasiewicz logic \L$_\infty$ is refined using enriched valuations that take into account the effect on $\phi$ of the stability of the…
We systematically study several versions of the disjunction and the existence properties in modal arithmetic. First, we newly introduce three classes $\mathrm{B}$, $\Delta(\mathrm{B})$, and $\Sigma(\mathrm{B})$ of formulas of modal…
In this paper we present a detailed study of the quantum conservation laws for Toda field theories defined on the half plane in the presence of a boundary perturbation. We show that total derivative terms added to the currents, while…
We investigate the set of Pi-1-2 sentences which are Pi-1-1 conservative over the theories of reverse mathematics RCA0+ISigma_n and ACA0. We exhibit new elements of these sets and conclude that the sets are Pi_2 complete. Along the way, we…
We investigate the problem $$-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \mathbf{n}} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} $$ where $\Omega$ is a bounded smooth…