We equip integral graded-polarized mixed period spaces with a natural $\mathbb{R}{\mathrm{alg}}$-definable analytic structure, and prove that any map associated to an admissible variation of Hodge structures is definable in $\mathbb{R}{\mathrm{an,exp}}$ respect this structure. As consequence we re-prove the zero loci normal functions are algebraic.

We distinguish between undefined terms as used in lambda definability of partial recursive functions and meaningless terms as used in infinite lambda calculus for the infinitary terms models that generalise the Böhm model. While there are uncountable many known sets of meaningless terms, there are four known sets of undefined terms. Two of these four are sets of meaningless terms. In this paper...

Reverse engineering problems for conjunctive queries (CQs), such as query by example (QBE) or definability, take a set of user examples and convert them into an explanatory CQ. Despite their importance, the complexity of these problems is prohibitively high (coNEXPTIME-complete). We isolate their two main sources of complexity and propose relaxations of them that reduce the complexity while hav...

Boban Veli ckovi c y Jensen's Coding Theorem provides a method for making a class of ordinals 2-deenable in a real. In this paper we explore the possibility of obtaining a 1-deenition. While this is not possible in general, we show that by assuming enough condensation, a class can be made 1 in a real parameter in a class-generic extension. Our main application is the following. Theorem There is...

Abstract This paper introduces the construct of an ultravaluation inspired by well-known ultraproduct. Basic properties and exemplary applications this notion are shown: for compactness definability theorems. We also use ultravaluations to check failure undefinability.