We are glad to announce the winners of the Christine Ladd-Franklin Logic Prize for the USA 2025 https://www.uni-log.org/christine-ladd-franklin-prize-of-logic-2025 ------------------------------------------------------------------------------------------------------------ Nathanael Ackerman (Harvard University, Cambridge, USA), & Cameron Freer (MIT, Cambridge, USA), & Mohammad Golshani (Institute for Research in Fundamental Sciences, Teheran, Iran) & Mostafa Mirabi (TheTaft School, Watertown, and Wesleyan University, Middletown, USA) & Rehana Patel (Wesleyan University, Middletown, USA) Title of the paper: Forcing with Invariant Measures Abstract. This paper introduces a model-theoretic generalization of the notion of forcing with random reals, in which forcing gives rise to random generic structures. Specifically, we consider forcing with κ-Borel probability measures on the space of L -structures with a (possibly uncountable) infinite set X, focusing on those that are invariant under the action of the symmetric group Sym(X). We demonstrate how any Sym(X)-invariant measure where X is countable can be uniquely extended to a Sym(Y )- invariant measure where Y is uncountable, and prove that forcing with such measures satisfies the countable chain condition. We also show that we can uniformly distinguish between these random generic structures and the Cohen generic structures that arise from forcing with a strong Fraïssé class: There is a κ-Borel set of low complexity that contains every Cohen generic structure that is not highly homogeneous but contains no random generic structure, implying that a structure that is not highly homogeneous cannot be both Cohen generic and random generic. Finally, we answer an open question of Kostana in the case of ω1, by establishing a connection between forcing with a strong Fraïssé class and Cohen forcing. ---------------------------------------------------------------------------------------------------------------------------- We have here a joint paper produced by a team of 5 people, four men (two Americans and two Iranians) and one woman (native of India), a good symbol of international cooperation. The paper is about forcing, a method developed by Paul Cohen (Stanford University) to prove the independence of the continuum hypothesis, a result for which he won the Fields medal in 1966 (the same year as Alexander Grothendieck). More recently, Maryam Mirzakhani (Stanford University) became the first Iranian as well as the first woman to win the Fields Medal (in 2014, the same year as Artur Avila). There is a strong mathematical tradition in Iran since the legendary Persian mathematician Al-Khwarizmi (790-850), who coined the word "algebra", and whose own personal name gave birth to "algorithm" and "algarismo". "Algarismo" is a Portuguese word used for the 10 numerals, often called "Arabic numerals", although they were imported from India by Al-Khwarizmi, who was Muslim but not Arab. At the 8th UNILOG, we will have an interesting workshop on notation organized by two colleagues from Argentina (Sandra Visokolskis and Gabriela Fulugonio): https://sites.google.com/view/unilog2025/workshops/philosophy-of-notation -------------------------------------------------------------------------------------------------- This is the first edition of the logic prize for the USA which I launched this year together with my colleagues Roy Cook and Jasmin Özel. We decided to give the name of Christine Ladd-Franklin (1847-1930) to this prize. Her PhD will soon be published in the series Logic PhDs of College Publications, Volume prepared by Ahti-Veikko Pietarinen and Amirouche Moktefi https://www.collegepublications.co.uk/lphd/ Following the spirit of the logic prizes, we formed a jury with people working in the US in all aspects of logic: philosophy, history, computer sciences, mathematics. Roger Maddux, one of the last PhD students of Alfred Tarski, was a member of this jury as well as Otávio Buneo, a Brazilian philosopher working in the USA for more than 20 years. ------------------------------------------------------------------------------------------------------- This paper will be published in the journal Logica Universalis and will represent the USA at the 3rd edition of the World Logic Prizes Contest which will take place during the 8th UNILOG in Cusco: https://sites.google.com/view/unilog2025/logic-prizes ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Prof. Dr. Dr. Jean-Yves Beziau Federal University of Rio de Janeiro, Brazil https://philpeople.org/profiles/jean-yves-beziau Creator of the Christine Ladd-Franklin prize of logic and director of the project A PRIZE OF LOGIC IN EVERY COUNTRY ! https://www.uni-log.org/logic-prize-world
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