The Mathematical Symbol "Models (⊧)"

The ⊧ Symbol in Mathematics: Models

The vast universe of mathematical symbols contains a rich set of notations, each playing a unique role in conveying certain concepts or relations. Among these, the ⊧ symbol, denoting "Models", holds specific significance, especially in the domain of mathematical logic. This article offers insights into the usage and relevance of the ⊧ symbol, supplemented with pertinent examples.

Usage

The ⊧ symbol is primarily employed in the realm of mathematical logic, particularly in model theory. It indicates that a certain structure (often called a model) satisfies a given formula or set of formulas.

Examples

  • Example 1: If \( M \) is a model and \( \phi \) is a formula, the relationship can be expressed as:
    \( M ⊧ \phi \)
    This means that the formula \( \phi \) holds true or is satisfied in the model \( M \).
  • Example 2: If \( T \) is a set of formulas and \( M \) is a model such that every formula in \( T \) holds true in \( M \), then:
    \( M ⊧ T \)
    This indicates that the model \( M \) satisfies every formula present in the set \( T \).

In essence, the ⊧ symbol serves as a bridge connecting structures (or models) to the formulas they satisfy. It is instrumental in expressing relationships in the context of mathematical logic and model theory, providing a compact notation for the concept of satisfaction.

Mathematical symbol 'Models'

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Codes for the ⊧ Symbol

The Symbol⊧
Alt CodeAlt 8871
HTML Code⊧
HTML Entity⊧
CSS Code\22A7
Hex Code⊧
UnicodeU+22A7

How To Insert the ⊧ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⊧ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8871. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8871;</b>My symbol: ⊧

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &models;</b>My symbol: ⊧

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
<style>
span:after {
content: "\22A7";}
</style>
<span>My symbol:</span> 		My symbol: ⊧

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x22A7;</b>My symbol: ⊧
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22A7 to place the ⊧ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output

⊧

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⊧ is U+22A7. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
TypeOutput
22A7
[Hold down Alt]
[Press x]		⊧
(The 22A7 turns into ⊧. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22A7. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22A7"
document.write("My symbol: " + str)		My symbol: ⊧