{"id":22,"date":"2017-12-09T18:39:08","date_gmt":"2017-12-09T22:39:08","guid":{"rendered":"http:\/\/sites.nd.edu\/rachaelalvir\/?page_id=22"},"modified":"2018-04-18T19:44:24","modified_gmt":"2018-04-18T23:44:24","slug":"rachael-alvir-personal-page","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/rachaelalvir\/","title":{"rendered":"Rachael Alvir &#8211; Personal Page"},"content":{"rendered":"<!-- RSPEAK_STOP --> <a href='http:\/\/wr.readspeaker.com\/webreader\/webreader.php?cid=&amp;t=wordpress&amp;url=https:\/\/sites.nd.edu\/rachaelalvir\/&amp;title=Rachael Alvir &#8211; Personal Page' onclick='readpage(this.href, 22); return false;'> <img src='http:\/\/graphics.readspeaker.com\/images\/wr\/listen_.gif' style='border-style: none;' alt=''><\/a><div id='WR_22'><\/div> <!-- RSPEAK_START --> <ul>\n<li><strong>Research<\/strong><\/li>\n<\/ul>\n<p>My interests in both mathematics and philosophy deal with circumventing G\u00f6del&#8217;s incompleteness theorems. In mathematical logic, I study\u00a0computable structure theory. I ask when it is possible to describe a structure up to isomorphism among models of the same cardinality in infinitary first-order languages, and compute exactly how difficult it is to give such a description when possible. My research also intersects with general recursion theory and set theory.\u00a0In philosophy, I am interested in G\u00f6del as a historical figure and fulfilling what I call &#8220;G\u00f6del&#8217;s Program:&#8221; defending the truth of the axioms of ZFC and the decidability of CH in some nonarbitrary formal system.<\/p>\n<p>My hair changes a lot, so you may not recognize me from time to time.<\/p>\n<ul>\n<li><strong>Publications<\/strong><\/li>\n<\/ul>\n<p>R. Alvir, D. Rossegger. &#8220;Scott Ranks of Scattered Linear Orders.&#8221; In preparation.<\/p>\n<p>R. Alvir, J. Knight, and C. McCoy. &#8220;Complexity of Scott Sentences.&#8221;\u00a0<em>Submitted. <\/em>(2017)<\/p>\n<p><a href=\"https:\/\/www.researchgate.net\/deref\/http%3A%2F%2Farxiv.org%2Fabs%2F1409.5840\">R. Alvir, S. Dever, B. Lovitz, J. Myer, C. Tamon, Y.Xu and H. Zhan. &#8220;Perfect State Transfer in Laplacian Quantum Walk.&#8221;\u00a0<em>Journal of Algebraic Combinatorics. <\/em>43:801-826 (2016)<\/a><\/p>\n<ul>\n<li><strong>Preprints and Notes<br \/>\n<\/strong><\/li>\n<\/ul>\n<p><a href=\"http:\/\/sites.nd.edu\/rachaelalvir\/files\/2017\/11\/NOTES.pdf\">A Short Introduction to Admissible Recursion Theory<\/a><\/p>\n<p><a href=\"https:\/\/arxiv.org\/abs\/1508.02432\">R. Alvir. &#8220;Zero Divisior Graphs of Quotient Rings.&#8221;\u00a0 <em>Preprint.<\/em>\u00a0(2015)<\/a><\/p>\n <!-- RSPEAK_STOP -->","protected":false},"excerpt":{"rendered":"<!-- RSPEAK_STOP --> <a href='http:\/\/wr.readspeaker.com\/webreader\/webreader.php?cid=&amp;t=wordpress&amp;url=https:\/\/sites.nd.edu\/rachaelalvir\/&amp;title=Rachael Alvir &#8211; Personal Page' onclick='readpage(this.href, 22); return false;'> <img src='http:\/\/graphics.readspeaker.com\/images\/wr\/listen_.gif' style='border-style: none;' alt=''><\/a><div id='WR_22'><\/div> <!-- RSPEAK_START --> <p>Research My interests in both mathematics and philosophy deal with circumventing G\u00f6del&#8217;s incompleteness theorems. In mathematical logic, I study\u00a0computable structure theory. I ask when it is possible to describe a structure up to isomorphism among models of the same cardinality in infinitary first-order languages, and compute exactly how difficult it is to give such a &hellip; <a href=\"https:\/\/sites.nd.edu\/rachaelalvir\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Rachael Alvir &#8211; Personal Page<\/span><\/a><\/p>\n <!-- RSPEAK_STOP -->","protected":false},"author":2467,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-22","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Rachael Alvir&#039;s Personal Research Page (University of Notre Dame)<\/title>\n<meta name=\"description\" content=\"Research My interests in both mathematics and philosophy deal with circumventing G\u00f6del&#039;s incompleteness theorems. In mathematical logic, I study\u00a0computable structure theory.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/sites.nd.edu\/rachaelalvir\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rachael Alvir&#039;s Personal Research Page (University of Notre Dame)\" \/>\n<meta property=\"og:description\" content=\"Research My interests in both mathematics and philosophy deal with circumventing G\u00f6del&#039;s incompleteness theorems. 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